Method, device, storage medium and computer equipment for predicting equilibrium point stability

Abstract

The present invention discloses a prediction method, device, storage medium, i.e., computer equipment, for the stability of a balance point, which relates to the biological field, and is mainly capable of improving the prediction accuracy of the stability of a balance point of a predator-predator community. The method includes: obtaining target attribute data corresponding to the predator-predator community to be predicted; determining the first fractional order growth function corresponding to the predator and the second fractional order growth function corresponding to the predator in the predator-predator community; based on the first fractional order growth function and the second fractional order growth function, determining the first number corresponding to the predator and the second number corresponding to the predator when the predator-predator community reaches a balance point, and determining a stability function matrix; judging whether the balance point of the predator-predator community is stable according to the first number, the second number, the stability function matrix, and the target attribute data. The present invention is suitable for predicting the stability of a balance point of a predator-predator community.

Description

Technical Field

[0001] The present invention relates to the biological field, and in particular to a method, device, storage medium and computer equipment for predicting the stability of an equilibrium point. Background Art

[0002] In biological systems, the predator-prey relationship is one of the most basic relationships. During the predation process, predators can not only directly kill prey, but also have indirect effects on prey, leading to changes in prey habitats, changes in foraging habits, and decreased reproductive rates. Therefore, in order to protect the ecological balance, it is necessary to determine the equilibrium point of the prey-predator community and whether the equilibrium point of the prey-predator community is stable.

[0003] At present, integer-order functions are usually used to predict the stability of the equilibrium point of the prey-predator community. However, integer-order functions can only describe the instantaneous changes of the prey-predator community, and the prey-predator community has characteristics such as memory and inheritance. Using integer-order functions to predict the stability of the equilibrium point will result in low prediction accuracy of the stability of the prey-predator community equilibrium point. Summary of the invention

[0004] The present invention provides a method, device, storage medium and computer equipment for predicting the stability of a balance point, which are mainly capable of improving the prediction accuracy of the stability of a predator-prey community balance point.

[0005] According to a first aspect of the present invention, there is provided a method for predicting the stability of an equilibrium point, comprising:

[0006] Obtain target attribute data corresponding to the prey-predator community to be predicted;

[0007] Determine a first fractional order growth function corresponding to the prey and a second fractional order growth function corresponding to the predator in the prey-predator community;

[0008] Based on the first fractional-order growth function and the second fractional-order growth function, determining a first quantity corresponding to the prey and a second quantity corresponding to the predators when the prey-predator community reaches an equilibrium point, and determining a stability function matrix corresponding to the prey-predator community;

[0009] Whether the equilibrium point of the predator-predator community is stable is determined according to the first quantity, the second quantity, the stability function matrix and the target attribute data.

[0010] According to a second aspect of the present invention, there is provided a device for predicting the stability of an equilibrium point, comprising:

[0011] An acquisition unit, used for acquiring target attribute data corresponding to the predator-predator community to be predicted;

[0012] A first determining unit is used to determine a first fractional order growth function corresponding to the prey and a second fractional order growth function corresponding to the predator in the prey-predator community;

[0013] A second determining unit is used to determine, based on the first fractional-order growth function and the second fractional-order growth function, a first number corresponding to the prey and a second number corresponding to the predators when the prey-predator community reaches an equilibrium point, and to determine a stability function matrix corresponding to the prey-predator community;

[0014] A determination unit is used to determine whether the equilibrium point of the predator-predator community is stable according to the first quantity, the second quantity, the stability function matrix and the target attribute data.

[0015] According to a third aspect of the present invention, there is provided a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the following steps:

[0016] Obtain target attribute data corresponding to the prey-predator community to be predicted;

[0017] Determine a first fractional order growth function corresponding to the prey and a second fractional order growth function corresponding to the predator in the prey-predator community;

[0018] Based on the first fractional-order growth function and the second fractional-order growth function, determining a first quantity corresponding to the prey and a second quantity corresponding to the predators when the prey-predator community reaches an equilibrium point, and determining a stability function matrix corresponding to the prey-predator community;

[0019] Whether the equilibrium point of the predator-predator community is stable is determined according to the first quantity, the second quantity, the stability function matrix and the target attribute data.

[0020] According to a fourth aspect of the present invention, there is provided a computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the program, the following steps are implemented:

[0021] Obtain target attribute data corresponding to the prey-predator community to be predicted;

[0022] Determine a first fractional order growth function corresponding to the prey and a second fractional order growth function corresponding to the predator in the prey-predator community;

[0023] Based on the first fractional-order growth function and the second fractional-order growth function, determining a first quantity corresponding to the prey and a second quantity corresponding to the predators when the prey-predator community reaches an equilibrium point, and determining a stability function matrix corresponding to the prey-predator community;

[0024] Whether the equilibrium point of the predator-predator community is stable is determined according to the first quantity, the second quantity, the stability function matrix and the target attribute data.

[0025] According to a method, device, storage medium and computer equipment for predicting the stability of a balance point provided by the present invention, compared with the current method of using integer-order functions to predict the stability of a prey-predator community balance point, the present invention obtains target attribute data corresponding to the prey-predator community to be predicted; and determines a first fractional-order growth function corresponding to the prey and a second fractional-order growth function corresponding to the predator in the prey-predator community; at the same time, based on the first fractional-order growth function and the second fractional-order growth function, determines a first number corresponding to the prey and a second number corresponding to the predator when the prey-predator community reaches a balance point, and determines a stability function matrix corresponding to the prey-predator community; and finally, according to the first fractional-order growth function, The method comprises the following steps: first, the first quantity, the second quantity, the stability function matrix and the target attribute data to determine whether the equilibrium point of the predator-predator community is stable, thereby determining the first quantity corresponding to prey and the second quantity corresponding to predators when the predator-predator community reaches the equilibrium point by utilizing the first fractional-order growth function and the second fractional-order growth function, and determining the stability function matrix corresponding to the predator-predator community. Finally, based on the target attribute data corresponding to the predator-predator community, the first quantity, the second quantity and the stability function matrix, it is determined whether the equilibrium point of the predator-predator community is stable, which comprehensively considers the memory and heredity characteristics of the predator-predator community, thereby improving the prediction accuracy of the stability of the equilibrium point of the predator-predator community. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] The drawings described herein are used to provide a further understanding of the present invention and constitute a part of this application. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation of the present invention. In the drawings:

[0027] Figure 1 A flow chart of a method for predicting the stability of a balance point provided by an embodiment of the present invention is shown;

[0028] Figure 2 A flow chart of another method for predicting the stability of a balance point provided by an embodiment of the present invention is shown;

[0029] Figure 3 The phase diagram and time series diagram of the equilibrium point of the predator-prey community are shown when f = 0, γ = 0.5, and q is 0.93 and 0.99 respectively;

[0030] Figure 4The phase diagram and time series diagram of the equilibrium point of the predator-prey community are shown when q = 0.93, f = 0, and γ is 0.66 and 0.33 respectively;

[0031] Figure 5 The phase diagram and time series diagram of the equilibrium point of the predator-prey community are shown when q = 0.93, γ = 0.33, and f is 1 and 0 respectively;

[0032] Figure 6 The phase diagram and time series diagram of the equilibrium point of the predator-prey community are shown when q = 0.93, γ = 0.66, and f is 1 and 0 respectively;

[0033] Figure 7 The phase diagram and timing diagram of the equilibrium point of the predator-prey community after adding the PD controller are shown when f = 0.93, γ = 0.5, q = 0.99.

[0034] Figure 8 A schematic diagram showing the structure of a device for predicting the stability of a balance point provided by an embodiment of the present invention is shown;

[0035] Fig. 9 A schematic diagram showing the structure of another device for predicting the stability of a balance point provided by an embodiment of the present invention is shown;

[0036] Fig.10 A schematic diagram of the physical structure of a computer device provided by an embodiment of the present invention is shown. DETAILED DESCRIPTION

[0037] The present invention will be described in detail below with reference to the accompanying drawings and in combination with embodiments. It should be noted that the embodiments and features in the embodiments of the present application can be combined with each other without conflict.

[0038] At present, the method of using integer-order functions to predict the stability of the equilibrium point of a prey-predator community cannot take into account the changes in all processes of the prey-predator community, resulting in low prediction accuracy of the stability of the equilibrium point of the prey-predator community.

[0039] In order to solve the above problems, an embodiment of the present invention provides a method for predicting the stability of a balance point, such as Figure 1 As shown, the method includes:

[0040] 101. Obtain target attribute data corresponding to the predator-predator community to be predicted.

[0041] Among them, there is a relationship of both interdependence and mutual restraint in the biological communities in nature. For example, population A relies on abundant natural resources for survival, and population B relies on resources other than A for survival, thus forming a prey-predator community, in which population A is the prey and population B is the predator.

[0042] For the embodiment of the present invention, in order to overcome the problem of low prediction accuracy of the stability of the equilibrium point of the predator-predator community in the prior art, the embodiment of the present invention determines the first number of prey and the second number of predators corresponding to the prey-predator community when the prey-predator community reaches the equilibrium point by utilizing the first fractional-order growth function and the second fractional-order growth function, and determines the stability function matrix corresponding to the prey-predator community. Finally, based on the target attribute data corresponding to the prey-predator community, the first number, the second number and the stability function matrix, it is determined whether the equilibrium point of the prey-predator community is stable, which comprehensively considers the memory and inheritance characteristics of the prey-predator community, thereby improving the prediction accuracy of the stability of the equilibrium point of the prey-predator community.

[0043] Specifically, the target attribute data include the birth rate of prey, the natural death rate of prey, the death rate of prey caused by competition, the capture rate of predators, the maximum growth rate of predators, the death rate of predators, and the degree of fear of predators by predators. As the prey-predator community is formed, the above target attribute data corresponding to the prey-predator community are stored in the biological database, which stores the target attribute data corresponding to various prey-predator systems. Therefore, in order to determine the stability of the equilibrium point of the prey-predator community, the birth rate of prey, the natural death rate of prey, the death rate of prey caused by competition, and the degree of fear of predators corresponding to the prey-predator community can be obtained in the biological database. The capture rate of the predator, the maximum growth rate of the predator, the mortality rate of the predator, and the degree of fear of the prey towards the predator. For example, the prey is the American rabbit and the predator is the bobcat. The corresponding birth rate of the American rabbit is 0.75, the natural mortality rate is 0.25, the mortality rate of the American rabbit competing here is 0.1, the capture rate of the bobcat on the American rabbit is 0.25, the maximum growth rate of the bobcat is 0.65, and the mortality rate of the bobcat is 0.35. Then, by calculating the stability condition when the prey-predator community is at the equilibrium point and the value range of the attribute data, it is finally determined whether the equilibrium point of the prey-predator community is stable. If it is unstable, measures are taken to stabilize the equilibrium point to avoid the extinction of the biological population.

[0044] 102. Determine a first fractional order growth function corresponding to prey and a second fractional order growth function corresponding to predators in the prey-predator community.

[0045] Among them, the first fractional order growth function is the growth rate function corresponding to the prey, the second fractional order growth function is the growth rate function corresponding to the predator, and the first fractional order growth function and the second fractional order growth function are specifically Hassell-Varley fractional order functional response functions.

[0046] Specifically, the Hassell-Varley fractional-order functional response function is based on the Kumar and Kumari integer-order functions, that is, the first fractional-order growth function corresponding to the prey and the second fractional-order growth function corresponding to the predator are obtained through the integer-order whole function. For example, in the prey-predator community, the prey is edible fish and the predator is a shark, then the first fractional-order growth function corresponding to the edible fish is determined, and the second fractional-order growth function corresponding to the shark is determined at the same time. Then, based on the target attribute data corresponding to the prey-predator community, the first fractional-order growth function and the second fractional-order growth function A fractional-order growth function is used to determine the first number of prey and the second number of predators when the prey-predator community is at an equilibrium point. At the same time, based on the first fractional-order growth function and the second fractional-order growth function, a stability function matrix corresponding to the prey-predator community is determined. Finally, based on the first number, the second number, the target attribute data, and the stability function matrix, whether the equilibrium point of the prey-predator community is stable is determined, which avoids the inability of integer-order functions to consider the memory and genetic characteristics of the prey-predator community, and improves the prediction accuracy of the stability of the equilibrium point of the prey-predator community.

[0047] 103. Based on the first fractional-order growth function and the second fractional-order growth function, determine a first number of prey and a second number of predators corresponding to the prey-predator community when the prey-predator community reaches an equilibrium point, and determine a stability function matrix corresponding to the prey-predator community.

[0048] The equilibrium point reached by the prey-predator community refers to the state in which the number of prey and the number of predators are both in a non-increasing and non-decreasing state.

[0049] For an embodiment of the present invention, the target attribute data is substituted into the first fractional-order growth function and the second fractional-order growth function. When the number of prey in the first fractional-order growth function is neither increasing nor decreasing, that is, the rate of change of the number corresponding to the prey is zero, and when the number of predators in the second fractional-order growth function is neither increasing nor decreasing, that is, the rate of change of the number corresponding to the prey is zero, the number of prey and the number of predators at this time are calculated, that is, the first number and the second number when the number of prey and predators reach a balance point. While calculating the first number corresponding to the prey and the second number corresponding to the predator, it is also necessary to determine the stability function matrix corresponding to the prey-predator community based on the first fractional-order growth function and the second fractional-order growth function. Specifically, the first fractional-order growth function and the second fractional-order growth function can be derivatively calculated, and multiple derivative functions obtained by calculation are determined as each element in the stability function matrix. Based on each element in the function matrix, the stability function matrix corresponding to the prey-predator community can be obtained.

[0050] 104. Determine whether the equilibrium point of the predator-predator community is stable according to the first quantity, the second quantity, the stability function matrix and the target attribute data.

[0051] For the embodiment of the present invention, after determining the first number and the second number when the number of prey and predators reaches the equilibrium point, in order to determine whether the first number and the second number can be maintained, that is, whether the equilibrium point is stable, it is necessary to bring the first number and the second number into the stability function matrix, and then calculate the sum of the main diagonal elements in the stability function, and take the opposite of the sum of the elements, and at the same time calculate the value of the determinant corresponding to the stability function matrix, and finally determine the stability condition of the equilibrium point based on the opposite of the sum of the elements and the value of the determinant, and finally judge whether the target attribute data corresponding to the prey-predator community meets the stability condition of the equilibrium point. If If the target attribute data satisfies the equilibrium point stability condition, it is determined that the equilibrium point of the prey-predator community is in a stable state, thereby determining the first number of prey and the second number of predators corresponding to the prey-predator community when the prey-predator community reaches the equilibrium point by utilizing the first fractional-order growth function and the second fractional-order growth function, and determining the stability function matrix corresponding to the prey-predator community, and finally determining whether the equilibrium point of the prey-predator community is stable based on the target attribute data corresponding to the prey-predator community, the first number, the second number and the stability function matrix, which comprehensively considers the memory and heredity characteristics of the prey-predator community, thereby improving the prediction accuracy of the stability of the equilibrium point of the prey-predator community.

[0052] According to a method for predicting the stability of an equilibrium point provided by the present invention, compared with the current method of predicting the stability of a prey-predator community equilibrium point using an integer-order function, the present invention obtains target attribute data corresponding to the prey-predator community to be predicted; and determines a first fractional-order growth function corresponding to the prey and a second fractional-order growth function corresponding to the predator in the prey-predator community; at the same time, based on the first fractional-order growth function and the second fractional-order growth function, determines a first quantity corresponding to the prey and a second quantity corresponding to the predator when the prey-predator community reaches an equilibrium point, and determines a stability function matrix corresponding to the prey-predator community; and finally determines the first quantity, the second quantity, and the stability function matrix according to the first quantity and the second quantity. The method comprises the following steps: first, a first quantity corresponding to prey and a second quantity corresponding to predators are determined by using the first fractional-order growth function and the second fractional-order growth function to determine whether the equilibrium point of the prey-predator community is stable, and second, a stability function matrix corresponding to the prey-predator community is determined. Finally, based on the target attribute data corresponding to the prey-predator community, the first quantity, the second quantity and the stability function matrix are used to determine whether the equilibrium point of the prey-predator community is stable. The memory and heredity characteristics of the prey-predator community are comprehensively considered to improve the prediction accuracy of the stability of the equilibrium point of the prey-predator community.

[0053] Further, in order to better illustrate the above process of predicting the stability of the equilibrium point of the predator-prey community, as a refinement and extension of the above embodiment, the embodiment of the present invention provides another method for predicting the stability of the equilibrium point, such as Figure 2 As shown, the method includes:

[0054] 201. Obtain target attribute data corresponding to the predator-predator community to be predicted.

[0055] Specifically, the prey in a prey-predator community is the prey, for example, rabbits are the prey and foxes are the predators. In order to study the stability of the equilibrium point of the rabbit-fox community, it is first necessary to obtain the birth rate of rabbits, the natural mortality rate of rabbits, the mortality rate of rabbits caused by competition, the capture rate of foxes, the maximum growth rate of foxes, the mortality rate of foxes, and the degree of fear of rabbits towards foxes in the community in the biological database. Then, based on the above data, the first number of rabbits and the second number of foxes when the number of rabbits and foxes reaches equilibrium are determined, and the equilibrium point stability function matrix corresponding to rabbits and foxes is determined at the same time. Finally, based on the first number of rabbits, the second number of foxes, the stability function matrix and the target attribute data, it is determined whether the rabbit-fox community is stable at the equilibrium point.

[0056] 202. Determine a first fractional order growth function corresponding to prey and a second fractional order growth function corresponding to predators in the prey-predator community.

[0057] For the embodiment of the present invention, in order to determine whether the equilibrium point of the prey-predator community is stable, it is first necessary to determine the first fractional-order growth function corresponding to the prey in the prey-predator community and the second fractional-order growth function corresponding to the predator. Based on this, step 202 specifically includes: determining the first integer-order growth function corresponding to the prey and the second integer-order growth function corresponding to the predator in the prey-predator community; determining the first fractional-order growth function corresponding to the prey based on the first integer-order growth function, and determining the second fractional-order growth function corresponding to the predator based on the second integer-order growth function.

[0058] Specifically, Kumar and Kumari proposed the following integer-order growth function:

[0059]

[0060]

[0061] Wherein, formula (1) represents the first integer order growth function corresponding to the prey, formula (2) represents the second integer order growth function corresponding to the predator, du / dt represents the growth rate corresponding to the prey, dv / dt represents the growth rate corresponding to the predator, u represents the number of prey corresponding to time t, v represents the number of predators corresponding to time t, r represents the birth rate corresponding to the prey, d1 represents the natural mortality rate corresponding to the prey, e is the mortality rate of the prey caused by competition, α represents the capture rate of the predator to the prey, a is a constant, β is the maximum growth rate of the predator, d2 is the mortality rate corresponding to the predator, f is the degree of fear of the prey to the predator, represents the Hassel-varley functional response function, γ is a constant, and the first integer-order growth function corresponding to the prey and the second integer-order growth function corresponding to the predator are transformed to obtain the first fractional-order growth function corresponding to the prey and the second fractional-order growth function corresponding to the predator, and the formula is as follows:

[0062]

[0063]

[0064] Among them, formula (3) represents the first fractional order growth function corresponding to the prey, formula (4) represents the second fractional order growth function corresponding to the predator, Dqu represents the first fractional order growth rate corresponding to the prey, and Dqv represents the second fractional order growth rate corresponding to the predator. Therefore, the first integer order growth function corresponding to the prey is used to determine the first fractional order growth function corresponding to the prey. At the same time, the second fractional order growth function corresponding to the predator is determined based on the second integer order growth function corresponding to the predator. Converting the integer order growth function into a fractional order growth function can avoid the situation that the integer order growth function can only study the instantaneous growth of the species population, thereby improving the prediction accuracy of the stability of the equilibrium point of the prey-predator community.

[0065] 203. Based on the first fractional-order growth function and the second fractional-order growth function, determine a first number corresponding to the prey and a second number corresponding to the predators when the prey-predator community reaches an equilibrium point.

[0066] The equilibrium point of the prey-predator community is when the growth rate of the prey is zero and the growth rate of the predator is also zero, that is, D in formula (3) q u is zero, D in formula (4) q v is zero.

[0067] For an embodiment of the present invention, after obtaining the first fractional-order growth function corresponding to the prey and the second fractional-order growth function corresponding to the predator, in order to calculate the first number corresponding to the prey and the second number corresponding to the predator when the prey-predator community reaches an equilibrium point, step 203 specifically includes: setting the growth amount corresponding to the prey in the first fractional-order growth function to zero, and obtaining a first equation with the number of prey and the number of predators as variables, and setting the growth amount corresponding to the predator in the second fractional-order growth function to zero, and obtaining a second equation with the number of prey and the number of predators as variables; calculating the solution of the equation corresponding to the first equation and the second equation, and determining the solution of the equation as the first number corresponding to the prey and the second number corresponding to the predator.

[0068] Among them, the growth amount corresponding to the prey is the fractional growth rate corresponding to the prey, and the growth amount corresponding to the predator is the growth rate corresponding to the predator.

[0069] Specifically, the calculation formulas for the first number of prey and the second number of predators are as follows:

[0070]

[0071]

[0072] Among them, equation (5) is expressed as the first equation with the number of prey and the number of predators as variables, and equation (6) is expressed as the second equation with the number of prey and the number of predators as variables. The number of prey and the number of predators that satisfy the above two equations are calculated, that is, the first number corresponding to the prey and the second number corresponding to the predators. By calculation, three equation solutions E0, E1 and E2 that satisfy the above two equations are obtained. The first solution is E0(0,0), and the second solution is The third correct solution is E2(u * , v * ), at the same time, through equations (5) and (6) we can get:

[0073]

[0074] When β>d2, v* is positive and u* can be found by the following equation:

[0075]

[0076] Among them, when When , u* is positive, so we get:

[0077]

[0078] Thus, according to the above method, the first number corresponding to the bait and the second number corresponding to the predator can be obtained.

[0079] 204. Calculate the derivative corresponding to the first fractional-order growth function to obtain a first derivative function corresponding to the first fractional-order growth function, and calculate the derivative corresponding to the second fractional-order growth function to obtain a second derivative function corresponding to the second fractional-order growth function.

[0080] For the embodiment of the present invention, after calculating the first number corresponding to the prey and the second number corresponding to the predator, it is also necessary to determine the stability function matrix corresponding to the prey-predator community based on the first fractional-order growth function and the second fractional-order growth function. The specific method for determining the stability function matrix corresponding to the prey-predator community is to firstly derive the above formula (3) with the number corresponding to the prey as a variable, that is, to derive the first fractional-order growth function, and obtain the first derivative function as follows:

[0081]

[0082] At the same time, the first fractional growth function is derived with the number of predators as the variable, and the first derivative function is obtained as follows:

[0083]

[0084] At the same time, the second fractional order growth number is derived with the number of prey as the variable, and the second derivative function is obtained as follows:

[0085]

[0086] At the same time, the second fractional growth function is derived with the number of predators as the variable, and the second derivative function is obtained as follows:

[0087]

[0088] 205. Determine a stability function matrix corresponding to the predator-predator community based on the first derivative function and the second derivative function.

[0089] Among them, the stability function matrix is ​​a Jacobian matrix. Specifically, after determining the first derivative function corresponding to the first fractional-order growth function and the second derivative function corresponding to the second fractional-order growth function, the first derivative function and the second derivative function are used as elements in the stability function evidence, and the stability function matrix corresponding to the predator-predator community is obtained as follows:

[0090]

[0091] 206. Determine whether the equilibrium point of the predator-predator community is stable according to the first quantity, the second quantity, the stability function matrix and the target attribute data.

[0092] For the embodiment of the present invention, after determining the first number of prey corresponding to the prey and the second number of predators corresponding to the predators when the number of prey and predators reaches equilibrium, as well as the stability function matrix corresponding to the prey-predator community, it is necessary to determine whether the equilibrium point of the prey-predator community is stable based on the first number, the second number, the target attribute data and the stability function matrix. Based on this, step 206 specifically includes: determining the attribute data value range when the equilibrium point of the prey-predator community is stable based on the first number, the second number and the stability function matrix; and determining whether the equilibrium point of the prey-predator community is stable based on the attribute data value range and the target attribute data.

[0093] Specifically, it can be seen from step 203 that the three corresponding equilibrium points of the predator-predator community are E0(0,0), E2(u * , v * ), where E0(0,0) indicates that when the prey-predator community reaches an equilibrium point, the first number corresponding to the prey is 0, and the second number corresponding to the predator is 0, It means that when the predator-predator community reaches the equilibrium point, the first quantity corresponding to the prey is The second number corresponding to the predator is 0, E2(u * , v * ) indicates that when the prey-predator community reaches the equilibrium point, the first number corresponding to the prey is u*, and the second number corresponding to the predator is v*, wherein u*>0, v* is greater than 0. Further, the stability of the equilibrium point E0 is first considered, and the first function matrix of the stability function matrix at E0 is as follows:

[0094]

[0095] From the above formula, it can be obtained that E0 is always a local stable node, which means that when the number of prey and predators is in the E0 attraction area, they will both become extinct.

[0096] Further, considering the stability of the equilibrium point E1, the second function matrix of the stable function matrix at E1 is as follows:

[0097]

[0098] Calculate the second function matrix J E1 The eigenvalues ​​of , it is found that the stability of the boundary equilibrium point E1 changes from a stable node to a saddle point, and its stability condition is β<d2. This behavior can be seen from the conditions for the existence of the positive equilibrium point E2. In summary, the equilibrium point E0 and the equilibrium point E1 do not conform to the law of the existence of predator-prey communities in the biological world.

[0099] Furthermore, only the equilibrium point E2 meets the conditions for the existence of populations in the biological world, so the stability of the equilibrium point E2 is analyzed in detail. The specific analysis method is that for the convenience of calculation, let x1 = uu*, x2 = vv*, move the equilibrium point to the origin of the coordinate system, and you can get the third fractional growth function and the fourth fractional full function of the first fractional growth function and the second fractional growth function at the origin. The specific formula is as follows:

[0100]

[0101]

[0102] Performing Laplace transformation on formula (7) and formula (8) yields the following formula:

[0103]

[0104]

[0105] Among them, L[u(t)] is the Laplace form of u at time t, L[v(t)] is the Laplace form of v at time t, and is the coefficient of the Laplace form, s q and q-1 is the convergence factor. For the convenience of calculation, the above formula is expressed in the following form:

[0106]

[0107] The parameters are,

[0108] in,

[0109]

[0110]

[0111]

[0112]

[0113] According to the above formula, the trace Tr and the determinant Det of the first fractional order growth function and the second fractional order growth function at the equilibrium point of E2(u*, v*) can be obtained as follows:

[0114]

[0115]

[0116] Among them, J E2 The characteristic equation of can be expressed as follows:

[0117] s 2q -(a 11 +a 22 )s q +a 11 a 22 -a 12 a 21 =0

[0118] It can be seen that if the equilibrium point E2 is in a stable state, it needs to satisfy Tr<0, Det>0, that is, the root of the JE2 characteristic equation is either a negative real root or a pair of complex conjugate roots with negative real parts. Therefore, the value range of the attribute data corresponding to the predator-prey community is as follows:

[0119]

[0120]

[0121] in,

[0122] Furthermore, after determining the value range of the attribute data when the predator-predator community reaches the equilibrium point, it is determined whether the target attribute data meets the above conditions. Based on this, the method includes: determining whether the target attribute data is within the value range of the attribute data; if the target attribute data is within the value range of the attribute data, it is determined that the equilibrium point of the predator-predator community is in a stable state.

[0123] Specifically, it is determined whether the target attribute data conforms to the attribute data value range. For example, if in the target attribute data, r is 0.375, d1 represents the natural mortality rate corresponding to the prey, e is 0.05, α is 0.25, a is a constant, β is 0.23, d2 is 0.13, and f is 0.99, and at the same time, u* is 00 and v* is 300 obtained by calculation, and the above data are substituted into the attribute data value range, and it is obtained that the above data satisfy the attribute data value range. Therefore, it can be known that the prey-predator community equilibrium point is in a stable state. Further, after determining whether the target attribute data is within the attribute data value range, the method also includes: if the target attribute data is not within the attribute data value range, it is determined that the equilibrium point of the prey-predator community is in an unstable state, that is, the target attribute data, the first quantity and the second quantity are substituted into the formula of the attribute data value range, and it is found that the attribute data range formula does not hold, then it is determined that the prey-predator community equilibrium point is unstable.

[0124] Furthermore, Hopf bifurcation refers to the change in stability of the equilibrium point of the predator-prey community and the emergence of a periodic solution. The critical value is called the Hopf bifurcation point. The predator-prey community experiences Hopf bifurcation near the equilibrium point for three bifurcation parameters: fractional order q, fear effect f, and interference coefficient λ. The Jacobian matrix at the equilibrium point E2(u*, v*) is:

[0125]

[0126] in,

[0127]

[0128]

[0129]

[0130]

[0131] The characteristic equation of equation (9) is:

[0132] λ 2q -(Tr)λ q +Det=0 (10)

[0133] in,

[0134] Tr=trace(J E2 )=(s q -s 11 (f))+(s q -s 22 (f))

[0135] Det=Det(J E2 )=(s q -s 11 (f))+(s q -s 22 (f))-s 12 (f)s 21 (f)

[0136] The two roots of equation (10) are

[0137]

[0138] When Hopf bifurcation occurs, the eigenvalues ​​of the Jacobian matrix (9) should be a pair of pure imaginary roots. Therefore, it is assumed that there exists f such that Tr(f) = 0, and for any f there exists Det(f) > 0. Therefore, at the critical point f = f * ,Tr=0, the characteristic equation (10) becomes:

[0139] λ 2q +Det(f * )=0 (11)

[0140] Here, f* represents the bifurcation point, so equation (11) must contain a pair of pure imaginary roots λ 1,2 = ±im 0 ,in i is the weight coefficient.

[0141] To prove the transversality condition, let f be at f * Nearby, λ 1,2 =u,v(f)±im(f), where,

[0142]

[0143] The transversality condition is:

[0144]

[0145] The equilibrium point of the prey-predator community is at the critical point f = f *Hopf bifurcation occurs at . In order to verify the correctness of the theory, we use numerical simulation to prove the existence of Hopf bifurcation and observe that Hopf bifurcation occurs under both bifurcation parameters q and γ.

[0146] Furthermore, in order to avoid bifurcation of the prey-predator community at the equilibrium point, a bifurcation controller can be added to the prey-predator community, wherein the bifurcation controller is a function formula that optimizes the stability performance of the equilibrium point so that the optimized prey-predator community can be stable in a larger range. After adding the controller, the first fractional order growth function corresponding to the prey and the second fractional order growth function corresponding to the predator are shown in the following formula:

[0147]

[0148] Among them, kp is the proportional gain coefficient, kd is the differential gain coefficient. As with the analysis method of the uncontrolled system, only the stability of the positive equilibrium point is analyzed here. 2 (u * , v * ) into the above formula with bifurcation controller and linearize it to obtain:

[0149]

[0150]

[0151] By performing Laplace transformation on formula (12) and formula (13), we can obtain:

[0152]

[0153] The characteristic equations of formula (12) and formula (13) are further obtained as follows:

[0154]

[0155] The characteristic equation above is equivalent to:

[0156] s 2q +L 1 s q +L 2 =0

[0157] in,

[0158]

[0159]

[0160] According to the Routh-Hurwitz stability criterion, it can be seen that when kp <d 2When kd<1 holds, the corresponding roots of formula (12) and formula (13) are all located in the left half plane of the complex plane. At this time, the positive equilibrium point of the fractional-order system is asymptotically stable.

[0161] For example, for an uncontrolled system, select r = 1, d 1 =0.5,e=0.1,α=1.1,m=1,β=1,d 2 =0.5, and select the initial values ​​U(0)=9.88 and V(0)=6.77, and discuss the influence of fractional order q, fear effect f and interference factor γ on the stability of the system. If f=0,γ=0.5, the fractional order q is taken as 0.93 and 0.99 respectively. By drawing the phase diagram and the time series diagram, it is found that when we increase the fractional order from 0.93 to 0.99, the equilibrium point of the predator-prey community changes from stable to limit cycle oscillation, such as Figure 3 As shown in Figure 2, changes in fractional order can cause Hopf bifurcation in the equilibrium point of the predator-prey community.

[0162] Furthermore, if q = 0.93, f = 0, and γ is 0.66 and 0.33, the phase diagram and time series diagram corresponding to the predator-predator community are drawn based on the above data, as shown in Figure 4 As shown in the figure, it can be seen from the changes in the figure that when the interference factor increases from 0.33 to 0.66, the equilibrium point of the predator-prey community changes from limit cycle oscillation to stability. It can be seen that the existence of certain interference factors is conducive to the continued survival of the population.

[0163] Furthermore, if q = 0.93, γ = 0.33, and f is 1 and 0, the phase diagram and time series diagram corresponding to the predator-prey community are drawn based on the above data, as shown in Figure 5 As shown in the figure, it can be seen from the changes in the figure that when the fear factor increases from 0 to 1, the stability of the equilibrium point of the predator-predator community will change. In actual situations, in most real prey-predator interactions, when the predators do not form a fixed number of tight groups, the interference coefficient is often 0.66. Even in the absence of fear, the predator-predator community shows stable focal dynamics at any of the three initial values. In order to fit the actual situation, a numerical simulation will be performed again when q = 0.93 and γ = 0.66, as shown in Figure 6 As shown, from the data shown in the figure, it can be obtained that when γ = 0.66, the change of the fear effect will not change the stability of the equilibrium point of the prey-predator community. Therefore, it is concluded that in the actual prey-predator community, the fear effect has no significant impact on the stability of the equilibrium point of the prey-predator community.

[0164] Furthermore, for the predator-predator community after adding the fractional controller, the parameters of the fractional controller are set to kp = -0.1, kd = 0.4, and the other parameter values ​​are the same as when the fractional controller is not added. When f = 0, γ = 0.5, q = 0.99, the phase diagram and timing diagram corresponding to the predator-predator community are as follows: Figure 7 As shown, compared Figure 3 and Figure 7 It can be seen that after adding the PD score controller, the equilibrium point of the prey-predator community has obviously become stable in an unstable position, which verifies the reasoning that the controller enhances the stability of the equilibrium point of the prey-predator community and achieves the purpose of controlling the equilibrium point of the prey-predator community to be stable in a larger range, thereby increasing the prediction accuracy of the stability of the equilibrium point of the prey-predator community.

[0165] Further, as Figure 1 In a specific implementation, an embodiment of the present invention provides a prediction device for the stability of a balance point, such as Figure 8 As shown, the device includes: an acquisition unit 31, a first determination unit 32, a second determination unit 33 and a judgment unit 34.

[0166] The acquisition unit 31 may be used to acquire target attribute data corresponding to the predator-predator community to be predicted.

[0167] The first determining unit 32 may be used to determine a first fractional order growth function corresponding to prey and a second fractional order growth function corresponding to predators in the prey-predator community.

[0168] The second determination unit 33 can be used to determine the first number of prey and the second number of predators corresponding to the prey-predator community when the prey-predator community reaches an equilibrium point based on the first fractional-order growth function and the second fractional-order growth function, and determine the stability function matrix corresponding to the prey-predator community.

[0169] The determination unit 34 may be configured to determine whether the equilibrium point of the predator-predator community is stable according to the first quantity, the second quantity, the stability function matrix and the target attribute data.

[0170] Specifically, in order to determine the first fractional order growth function corresponding to the prey and the second fractional order growth function corresponding to the predator in the prey-predator community, as follows Fig. 9 As shown, the first determination unit 32 can be specifically used to determine a first integer-order growth function corresponding to the prey and a second integer-order growth function corresponding to the predator in the prey-predator community; determine a first fractional-order growth function corresponding to the prey based on the first integer-order growth function, and determine a second fractional-order growth function corresponding to the predator based on the second integer-order growth function.

[0171] In a specific application scenario, in order to determine the first number of prey and the second number of predators corresponding to the prey when the prey-predator community reaches a balance point, the second determination unit 33 includes a setting module 331 and a calculation module 332 .

[0172] The setting module 331 can be used to set the growth amount corresponding to the prey in the first fractional-order growth function to zero, so as to obtain a first equation with the number of prey and the number of predators as variables, and to set the growth amount corresponding to the predators in the second fractional-order growth function to zero, so as to obtain a second equation with the number of prey and the number of predators as variables.

[0173] The calculation module 332 may be used to calculate a solution corresponding to the first equation and the second equation, and determine the solution as a first number corresponding to the prey and a second number corresponding to the predator.

[0174] In a specific application scenario, in order to determine the stability function matrix corresponding to the predator-predator community, the second determination unit 33 further includes a determination module 333 .

[0175] The calculation module 332 can also be used to calculate the derivative corresponding to the first fractional-order growth function to obtain the first derivative function corresponding to the first fractional-order growth function, and calculate the derivative corresponding to the second fractional-order growth function to obtain the second derivative function corresponding to the second fractional-order growth function.

[0176] The determination module 333 may be configured to determine a stability function matrix corresponding to the predator-predator community based on the first derivative function and the second derivative function.

[0177] In a specific application scenario, in order to determine whether the equilibrium point of the predator-predator community is stable, the determination unit 34 can be specifically used to determine the attribute data value range when the equilibrium point of the predator-predator community is stable based on the first quantity, the second quantity and the stability function matrix; based on the attribute data value range and the target attribute data, determine whether the equilibrium point of the predator-predator community is stable.

[0178] In a specific application scenario, in order to determine whether the equilibrium point of the predator-predator community is stable based on the attribute data value range and the target attribute data, the determination unit 34 can be specifically used to determine whether the target attribute data is within the attribute data value range; if the target attribute data is within the attribute data value range, it is determined that the equilibrium point of the predator-predator community is in a stable state.

[0179] In a specific application scenario, after determining whether the target attribute data is within the attribute data value range, the determination unit 34 can also be used to determine that the equilibrium point of the predator-prey community is in an unstable state if the target attribute data is not within the attribute data value range.

[0180] It should be noted that for other corresponding descriptions of the functional modules involved in the device for predicting the stability of a balance point provided in an embodiment of the present invention, reference can be made to Figure 1 The corresponding description of the method shown will not be repeated here.

[0181] Based on the above Figure 1 The method shown, accordingly, an embodiment of the present invention also provides a computer-readable storage medium, on which a computer program is stored, and when the program is executed by a processor, the following steps are implemented: obtaining target attribute data corresponding to the prey-predator community to be predicted; determining a first fractional-order growth function corresponding to the prey and a second fractional-order growth function corresponding to the predator in the prey-predator community; based on the first fractional-order growth function and the second fractional-order growth function, determining a first number corresponding to the prey and a second number corresponding to the predator when the prey-predator community reaches an equilibrium point, and determining a stability function matrix corresponding to the prey-predator community; judging whether the equilibrium point of the prey-predator community is stable based on the first number, the second number, the stability function matrix and the target attribute data.

[0182] Based on the above Figure 1 The method shown and Figure 8 The embodiment of the device shown in the figure, the embodiment of the present invention also provides a physical structure diagram of a computer device, such as Fig.10 As shown, the computer device includes: a processor 41, a memory 42, and a computer program stored in the memory 42 and executable on the processor, wherein the memory 42 and the processor 41 are both arranged on a bus 43, and when the processor 41 executes the program, the following steps are implemented: obtaining target attribute data corresponding to the prey-predator community to be predicted; determining a first fractional-order growth function corresponding to the prey and a second fractional-order growth function corresponding to the predator in the prey-predator community; determining a first quantity corresponding to the prey and a second quantity corresponding to the predator when the prey-predator community reaches an equilibrium point based on the first fractional-order growth function and the second fractional-order growth function, and determining a stability function matrix corresponding to the prey-predator community; determining whether the equilibrium point of the prey-predator community is stable based on the first quantity, the second quantity, the stability function matrix and the target attribute data.

[0183] Through the technical solution of the present invention, the present invention obtains the target attribute data corresponding to the prey-predator community to be predicted; and determines the first fractional order growth function corresponding to the prey and the second fractional order growth function corresponding to the predator in the prey-predator community; at the same time, based on the first fractional order growth function and the second fractional order growth function, determines the first number corresponding to the prey and the second number corresponding to the predator when the prey-predator community reaches an equilibrium point, and determines the stability function matrix corresponding to the prey-predator community; finally, according to the first number, the second number, the stability function matrix and the target attribute data, judges Determine whether the equilibrium point of the prey-predator community is stable, thereby determining the first number of prey corresponding to the prey and the second number of predators corresponding to the prey-predator community when the prey-predator community reaches the equilibrium point by using the first fractional-order growth function and the second fractional-order growth function, and determining the stability function matrix corresponding to the prey-predator community, and finally based on the target attribute data corresponding to the prey-predator community, the first number, the second number and the stability function matrix, determine whether the equilibrium point of the prey-predator community is stable, comprehensively considering the memory and heredity characteristics of the prey-predator community, and improving the prediction accuracy of the stability of the equilibrium point of the prey-predator community.

[0184] Obviously, those skilled in the art should understand that the above modules or steps of the present invention can be implemented by a general computing device, they can be concentrated on a single computing device, or distributed on a network composed of multiple computing devices, and optionally, they can be implemented by a program code executable by a computing device, so that they can be stored in a storage device and executed by the computing device, and in some cases, the steps shown or described can be executed in a different order than here, or they can be made into individual integrated circuit modules, or multiple modules or steps therein can be made into a single integrated circuit module for implementation. Thus, the present invention is not limited to any specific combination of hardware and software.

[0185] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for predicting the stability of equilibrium points, It is characterized in that include: Obtain target attribute data corresponding to the prey-predator community to be predicted; Determine a first fractional order growth function corresponding to the prey and a second fractional order growth function corresponding to the predator in the prey-predator community; The growth amount corresponding to the prey in the first fractional order growth function is set to zero, so as to obtain a first equation with the number of prey and the number of predators as variables, and the growth amount corresponding to the predator in the second fractional order growth function is set to zero, so as to obtain a second equation with the number of prey and the number of predators as variables; Calculating a solution of the first equation and the second equation, and determining the solution of the equation as a first quantity corresponding to the prey and a second quantity corresponding to the predator; Calculating the derivative corresponding to the first fractional-order growth function to obtain a first derivative function corresponding to the first fractional-order growth function, and calculating the derivative corresponding to the second fractional-order growth function to obtain a second derivative function corresponding to the second fractional-order growth function; Determining a stability function matrix corresponding to the predator-predator community based on the first derivative function and the second derivative function; Whether the equilibrium point of the predator-predator community is stable is determined according to the first quantity, the second quantity, the stability function matrix and the target attribute data.

2. The method according to claim 1, It is characterized in that The step of determining a first fractional order growth function corresponding to the prey and a second fractional order growth function corresponding to the predator in the prey-predator community comprises: Determine a first integer order growth function corresponding to the prey and a second integer order growth function corresponding to the predator in the prey-predator community; Based on the first integer-order growth function, a first fractional-order growth function corresponding to the prey is determined, and based on the second integer-order growth function, a second fractional-order growth function corresponding to the predator is determined.

3. The method according to claim 1, It is characterized in that The determining whether the equilibrium point of the predator-predator community is stable according to the first quantity, the second quantity, the stability function matrix and the target attribute data includes: Determine, according to the first quantity, the second quantity and the stability function matrix, a value range of the attribute data when the equilibrium point of the predator-prey community is stable; Based on the attribute data value range and the target attribute data, it is determined whether the equilibrium point of the predator-predator community is stable.

4. The method according to claim 3, It is characterized in that The determining whether the equilibrium point of the predator-predator community is stable based on the attribute data value range and the target attribute data includes: Determine whether the target attribute data is within the attribute data value range; If the target attribute data is within the attribute data value range, it is determined that the equilibrium point of the predator-predator community is in a stable state.

5. The method according to claim 4, It is characterized in that After determining whether the target attribute data is within the attribute data value range, the method further includes: If the target attribute data is not within the attribute data value range, it is determined that the equilibrium point of the predator-predator community is in an unstable state.

6. A device for predicting the stability of an equilibrium point, It is characterized in that include: An acquisition unit, used for acquiring target attribute data corresponding to the predator-predator community to be predicted; A first determining unit is used to determine a first fractional order growth function corresponding to the prey and a second fractional order growth function corresponding to the predator in the prey-predator community; A second determination unit is used to set the growth amount corresponding to the prey in the first fractional order growth function to zero, so as to obtain a first equation with the number of prey and the number of predators as variables, and to set the growth amount corresponding to the predator in the second fractional order growth function to zero, so as to obtain a second equation with the number of prey and the number of predators as variables; Calculate the solution of the equation corresponding to the first equation and the second equation, and determine the solution of the equation as a first number corresponding to the prey and a second number corresponding to the predator; calculate the derivative corresponding to the first fractional-order growth function to obtain a first derivative function corresponding to the first fractional-order growth function, and calculate the derivative corresponding to the second fractional-order growth function to obtain a second derivative function corresponding to the second fractional-order growth function; determine the stability function matrix corresponding to the prey-predator community based on the first derivative function and the second derivative function; A determination unit is used to determine whether the equilibrium point of the predator-predator community is stable according to the first quantity, the second quantity, the stability function matrix and the target attribute data.

7. A computer-readable storage medium having a computer program stored thereon, It is characterized in that When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 5 are implemented.

8. A computer device comprising a memory, a processor and a computer program stored in the memory and executable on the processor, It is characterized in that When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 5 are implemented.

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