Ecological system dynamic characteristic analysis method and device

Abstract

The invention provides an ecological system dynamic characteristic analysis method and device, and the method comprises the steps: constructing a deterministic model of an ecological system, and constructing a random model of the ecological system based on the deterministic model, the deterministic model comprising a plurality of key variables in the ecological system; respectively defining the global asymptotic stability of the deterministic model, the global positive solution existence of the random model and the population durability of the ecological system; and determining a value relation among the key variables when the ecological system meets the global asymptotic stability, the global positive solution existence and the population persistence, so as to realize dynamic characteristic analysis of the ecological system. By adopting the method, the dynamic characteristics of the ecological system can be accurately, effectively and comprehensively analyzed.

Description

Technical Field

[0001] The present invention relates to the technical field of ecosystems, and in particular to a method and device for analyzing dynamic characteristics of an ecosystem. Background Art

[0002] With the deep intervention of human activities in natural ecosystems, the interactions between species in ecosystems are becoming increasingly complex, especially the relationship between prey and predators. Although the traditional prey-predator model provides us with a certain theoretical basis, its explanatory and predictive power is limited when facing the complex interactions in real ecosystems. First, the fear effect is an important factor in the ecosystem that cannot be ignored. When facing predators, prey often feel fear, which not only affects the behavior of prey, but also indirectly affects the stability of the entire ecosystem. However, traditional models often ignore this important factor. Secondly, prey refuges are widely present in real ecosystems. When facing predator pressure, prey will look for refuges to avoid being hunted by predators. The existence of such refuges has an important impact on the stability of the ecosystem and the coexistence mechanism of species, but traditional models often fail to fully consider it. Finally, feedback control is a basic mechanism in the ecosystem. The various components in the ecosystem jointly maintain the stability and balance of the ecosystem through interactions and feedback regulation. However, traditional models often oversimplify or ignore this mechanism when describing it. It can be seen that the existing prey-predator model cannot accurately, effectively and comprehensively analyze the dynamic characteristics of the ecosystem. Therefore, how to accurately, effectively and comprehensively analyze the dynamic characteristics of the ecosystem has become an urgent problem that needs to be solved. Summary of the invention

[0003] In view of this, an object of the present invention is to provide a method and device for analyzing the dynamic characteristics of an ecosystem, so as to achieve accurate, effective and comprehensive analysis of the dynamic characteristics of an ecosystem.

[0004] In a first aspect, an embodiment of the present application provides a method for analyzing dynamic characteristics of an ecosystem, the method comprising:

[0005] Constructing a deterministic model of an ecosystem, and constructing a stochastic model of the ecosystem based on the deterministic model, wherein the deterministic model includes several key variables in the ecosystem;

[0006] The global asymptotic stability of the deterministic model, the existence of global positive solutions of the stochastic model, and the population persistence of the ecosystem are defined respectively;

[0007] The value relationship between the key variables of the ecosystem when satisfying the global asymptotic stability, the existence of the global correct solution and the population persistence is determined to realize the dynamic characteristic analysis of the ecosystem.

[0008] Optionally, the deterministic model of building an ecosystem includes:

[0009] The deterministic model is constructed according to population information, fear levels, and refuge rates of various populations in the ecosystem, wherein the populations include prey and predators.

[0010] Optionally, the deterministic model is:

[0011]

[0012] Where x represents the prey density, x(t) represents the prey density at time t, y(t) represents the predator density, y(t) represents the predator density at time t, and u i (t)(i=1,2) represents the control variable. When i=1, u i (t) represents the control variable of the prey. When i=2, u i (t) represents the control variable of the predator; α is the intrinsic growth rate of the prey, b is the environmental carrying capacity of the prey, K represents the fear level, β represents the predator's ability to capture the prey, c is the conversion rate of the predator's prey, m represents the shelter rate, e is the first decay rate of the control variable, g is the second decay rate of the control variable, f represents the average effect of the prey on the disturbance rate, h represents the average effect of the predator on the disturbance rate, and n i (i=1,2) is the perturbation rate coefficient. When i=1, n i represents the disturbance rate coefficient experienced by the prey. When i = 2, n i represents the disturbance rate coefficient experienced by the predator, r is the predator population density constraint coefficient, and a is the half-saturation coefficient of the prey population.

[0013] Optionally, constructing the stochastic model of the ecosystem based on the deterministic model includes:

[0014] White noise defined in complete probability space;

[0015] The deterministic model constructs a stochastic model of the ecosystem, and the stochastic model is constructed according to the white noise and the noise intensity of the white noise.

[0016] In a second aspect, an embodiment of the present application provides an ecosystem dynamic characteristics analysis device, the device comprising:

[0017] An ecosystem model construction module, used to construct a deterministic model of the ecosystem, and to construct a stochastic model of the ecosystem based on the deterministic model, wherein the deterministic model includes several key variables in the ecosystem;

[0018] A dynamic characteristic definition module, used to define the global asymptotic stability of the deterministic model, the existence of global positive solutions of the stochastic model, and the population persistence of the ecosystem;

[0019] The dynamic characteristic analysis module is used to determine the value relationship between key variables when the ecosystem satisfies the global asymptotic stability, the existence of the global correct solution and the population persistence, so as to realize the dynamic characteristic analysis of the ecosystem.

[0020] Optionally, the deterministic model of building an ecosystem includes:

[0021] The deterministic model is constructed according to population information, fear levels, and refuge rates of various populations in the ecosystem, wherein the populations include prey and predators.

[0022] Optionally, the deterministic model is:

[0023]

[0024] Where x represents the prey density, x(t) represents the prey density at time t, y(t) represents the predator density at time t, and u i (t)(i=1,2) represents the control variable. When i=1, u i (t) represents the control variable of the prey. When i=2, u i (t) represents the control variable of the predator; α is the intrinsic growth rate of the prey, b is the environmental carrying capacity of the prey, K represents the fear level, β represents the predator's ability to capture the prey, c is the conversion rate of the predator's prey, m represents the shelter rate, e is the first decay rate of the control variable, g is the second decay rate of the control variable, f represents the average effect of the prey on the disturbance rate, h represents the average effect of the predator on the disturbance rate, and n i (i=1,2) is the perturbation rate coefficient. When i=1, n i represents the disturbance rate coefficient experienced by the prey. When i = 2, n i represents the disturbance rate coefficient experienced by the predator, r is the predator population density constraint coefficient, and a is the half-saturation coefficient of the prey population.

[0025] Optionally, constructing the stochastic model of the ecosystem based on the deterministic model includes:

[0026] White noise defined in complete probability space;

[0027] The deterministic model constructs a stochastic model of the ecosystem, and the stochastic model is constructed according to the white noise and the noise intensity of the white noise.

[0028] The technical solution provided by this application includes but is not limited to the following beneficial effects:

[0029] This application constructs a deterministic model of an ecosystem, and constructs a stochastic model of the ecosystem based on the deterministic model, wherein the deterministic model contains several key variables in the ecosystem, and can comprehensively consider the impact of multiple factors such as fear effect, prey shelter and feedback control on the ecosystem, so that the model is closer to the complexity of the actual ecosystem. Then, the global asymptotic stability of the deterministic model, the existence of the global positive solution of the stochastic model, and the population persistence of the ecosystem are defined respectively, and the value relationship between the key variables of the ecosystem when the global asymptotic stability, the existence of the global positive solution and the population persistence are determined. The model can be applied to multiple fields such as ecosystem stability assessment, species coexistence mechanism research and ecological restoration and reconstruction, and provide practical tools and methods for the management and protection of the ecosystem. Because the model has a strong multi-scenario simulation capability, it can simulate the dynamic change process of the ecosystem under different scenarios. This ability makes the model more flexible and practical in dealing with different ecological and environmental problems and formulating management strategies. At the same time, the variables such as fear effect, prey shelter and feedback control in the model are simulated by refined parameter settings to simulate their actual effects. These parameters can be adjusted and optimized according to the specific conditions of different ecosystems, thereby improving the applicability and accuracy of the model. Finally, the relationship between the values ​​of key variables when the ecosystem meets the global asymptotic stability, the existence of global positive solutions and the persistence of populations is determined to achieve accurate, effective and comprehensive analysis of the dynamic characteristics of the ecosystem.

[0030] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, preferred embodiments are given below and described in detail with reference to the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for use in the embodiments are briefly introduced below. It should be understood that the following drawings only show certain embodiments of the present invention and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other related drawings can be obtained based on these drawings without creative work.

[0032] Figure 1 A flow chart of a method for analyzing dynamic characteristics of an ecosystem provided by Embodiment 1 of the present invention is shown;

[0033] Figure 2 A flow chart of a random model construction method provided by the first embodiment of the present invention is shown;

[0034] Figure 3 A schematic diagram of the structure of an ecosystem dynamic characteristics analysis device provided by Embodiment 2 of the present invention is shown. DETAILED DESCRIPTION

[0035] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. The components of the embodiments of the present invention generally described and shown in the drawings here can be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the drawings is not intended to limit the scope of the claimed invention, but merely represents selected embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without making creative work belong to the scope of protection of the present invention.

[0036] Embodiment 1

[0037] Explanation of terms related to this application:

[0038] 1. Fear effect: A factor that affects the interaction between predators and prey, usually used to describe how the predator's hunting behavior on prey is affected by the prey's fear or avoidance behavior of its potential predator. This effect can be represented by parameters in mathematical models. For example, in a predator-prey model, the fear effect may be reflected by an additional function or parameter to explain the change in the prey's behavior pattern when it perceives the presence of a predator.

[0039] 2. Prey refuge: A safe area or resource that a prey population can use to reduce the risk of predation when facing predator pressure. This type of refuge usually refers to a place where prey can hide or protect themselves, such as a hidden habitat, an area that is not easily accessible to predators, or has specific protection measures. In mathematical models, prey refuges can be modeled as an additional parameter or function to describe the probability or effect of prey choosing to use a refuge, and the impact of this choice on predator-prey dynamics. Increasing the number or effectiveness of prey refuges will usually reduce the successful predation rate of predators, thereby affecting the stability and dynamic changes of the entire system.

[0040] 3. Feedback control refers to a strategy that affects the dynamics of biological populations by adjusting the environment or behavior. This control strategy can affect the interaction and overall stability of populations by changing population density or other biological characteristics. In the predator-prey model, feedback control can affect the dynamic balance between predators and prey by adjusting the relative number, predation rate, reproduction rate, etc. This control strategy can help maintain the stability of the ecosystem and prevent problems such as over-predation or over-reproduction.

[0041] 4. Global asymptotic stability: It means that after a period of time, no matter what the initial conditions are, the state of the system will eventually tend to a specific equilibrium state or orbit, that is, the system will converge to this state and remain stable near this state.

[0042] 5. Descartes' Rule of Sgins is a mathematical tool used to analyze the number of positive and negative roots of high-order polynomials.

[0043] 6. Lyapunov function: It is usually used to analyze the asymptotic stability or non-asymptotic stability of a dynamic system. The basic idea is to quantify a certain energy or potential energy of the system state by constructing a scalar function V(x), where x represents the system state.

[0044] 7.M matrix: It is a special L matrix whose inverse matrix is ​​a non-negative matrix, the real part of all eigenvalues ​​is greater than zero, and all principal minors and sequential principal minors are positive.

[0045] 8. Local Lipschitz continuity: When solving differential equations, the existence and uniqueness of the solution are guaranteed.

[0046] 9. The basic idea of ​​Ito's formula is to generalize the chain rule, multiplication rule, and integration rule in calculus to random processes. Through Ito's lemma, we can calculate the derivatives, integrals, and other differential quantities of random processes, thereby gaining a deeper understanding of the evolution of random processes.

[0047] To facilitate understanding of this application, Figure 1 The flowchart of a method for analyzing dynamic characteristics of an ecosystem provided by the first embodiment of the present invention is shown to describe the contents of the first embodiment of the present application in detail.

[0048] See also Figure 1 As shown, Figure 1A flowchart of a method for analyzing dynamic characteristics of an ecosystem provided by the first embodiment of the present invention is shown, wherein the method comprises steps S101 to S103:

[0049] S101: constructing a deterministic model of an ecosystem, and constructing a stochastic model of the ecosystem based on the deterministic model, wherein the deterministic model includes several key variables in the ecosystem.

[0050] Specifically, we first construct a deterministic model with key variables such as fear effect, prey refuge, and feedback control, as follows:

[0051]

[0052] Where x represents the prey density, y represents the predator density, x(t) represents the prey density at time t, y(t) represents the predator density at time t, and u i (t)(i=1,2) represents the control variable. When i=1, u i (t) represents the control variable of the prey. When i=2, u i (t) represents the control variable of the predator; α is the intrinsic growth rate of the prey, b is the environmental carrying capacity of the prey, K represents the fear level, β represents the predator's ability to capture the prey, c is the conversion rate of the predator's prey, m represents the shelter rate, e is the first decay rate of the control variable, g is the second decay rate of the control variable, f represents the average effect of the prey on the disturbance rate, h represents the average effect of the predator on the disturbance rate, and n i (i=1,2) is the perturbation rate coefficient. When i=1, n i represents the disturbance rate coefficient experienced by the prey. When i = 2, n i represents the disturbance rate coefficient experienced by the predator, r is the predator population density constraint coefficient, and a is the half-saturation coefficient of the prey population.

[0053] Define white noise to simulate environmental disturbances in the ecosystem, and build a random model of the ecosystem based on the above deterministic model. The specific random model is:

[0054]

[0055] in, represents white noise, when i=1, represents the influence of white noise on the prey population. When i=2, represents the white noise effect on the predator population, B i (t) is a standard Brownian motion defined on the complete probability space (Ω, F, P). It satisfies the initial conditions B1(0) = 0, B2(0) = 0, σ i(i=1,2) represents the standard deviation of white noise. When i=1, σ i represents the standard deviation of the white noise to which the prey population is subjected. When i = 2, σ i represents the standard deviation of the white noise to which the predator population is subjected, where is the intensity of the white noise.

[0056] S102: defining the global asymptotic stability of the deterministic model, the existence of global positive solutions of the stochastic model, and the population persistence of the ecosystem respectively.

[0057] S103: Determine the value relationship between key variables of the ecosystem when the ecosystem satisfies the global asymptotic stability, the existence of the global correct solution and the population persistence, so as to realize the dynamic characteristic analysis of the ecosystem.

[0058] Specifically, the global asymptotic stability, the existence of global positive solutions of the stochastic model, and the population persistence of the ecosystem are analyzed and proved.

[0059] First, the positivity of the equilibrium point and the global asymptotic stability of the internal equilibrium point are defined for the deterministic model. The boundary equilibrium point of the deterministic model is:

[0060]

[0061] The internal equilibrium point of the deterministic model is Among them, x * is the value of the prey population in the internal equilibrium point, y * The value of the predator population in the internal equilibrium point, is the value of the feedback control variable on the prey population, is the value of the feedback control variable on the predator population, and d is the mortality rate of the predator.

[0062] According to Descartes' Rule of Sgins, the uniqueness of the internal equilibrium point is obtained. In order to prove the global asymptotic stability of the unique internal equilibrium point, the Lyapunov function is introduced to judge the asymptotic stability of the internal equilibrium point. The specific function V(t) is:

[0063]

[0064] Among them, p i ,q i (i=1,2) is a positive constant; when i=1, p i represents the coefficient of the prey term in the constructed Lyapunov function, q irepresents the coefficient of the feedback control variable term of the prey in the constructed Lyapunov function; when i = 2, p i represents the coefficient of the predator term in the constructed Lyapunov function, q i represents the coefficient of the feedback control variable term of the predator in the constructed Lyapunov function; by calculation, using the existence and uniqueness of the internal equilibrium point and the Lyapunov asymptotic stability theorem, the internal equilibrium point E can be obtained. * The global asymptotic stability of , u1 is the control variable of the prey, and u2 is the control variable of the predator.

[0065] For the random model, the existence of its global positive solution is first proved as follows:

[0066] Since the coefficients of the random model satisfy the local Lipschitz continuity, in the interval [0,τ e ], there is a unique local positive solution (x(t), y(t), u1(t), u2(t)). In order to derive the globality of this solution, it is necessary to prove that the outbreak time τ e =∞ is almost certain (as). Without loss of generality, define the stopping time τ k :

[0067]

[0068] or max{x(t),y(t),u1(t),u2(t)}≥k;

[0069] Among them, k is a constant, x(t), y(t), u1(t), and u2(t) represent the density of prey, predator, feedback control variables of prey, and feedback control variables of predator in the system at time t respectively.

[0070] Then, we have τ k As k→∞ increases. Let Obviously, there is τ ∞ ≤τ e Now, we must prove that τ ∞ =∞ is almost certain. Using proof by contradiction, assuming that τ ∞ =∞ does not hold, construct a suitable Lyapunov function: τ ∞ is the stopping time τ k The limit as k→+∞.

[0071] Using Ito's formula, we can get: Let k→∞, and we get a contradiction. This proves the existence of a global positive solution to the random model. x(0), y(0), u1(0), u2(0) represent the initial values ​​of the prey, predator, feedback control variables of the prey, and feedback control variables of the predator in the system, respectively.

[0072] Next, consider the internal equilibrium point of the deterministic model The asymptotic properties of random models are discussed here.

[0073] Assume that (x(t), y(t), u1(t), u2(t)) is a random model with arbitrary initial values If it satisfies: as well as Then this solution has the following properties:

[0074]

[0075] in, represents a 4-dimensional positive real number space, E represents expectation, and θ represents an arbitrary value parameter.

[0076] Next, we define the persistence criterion of the random model, which is a key step in controlling the stability of the ecosystem. First, we give the definition of population persistence:

[0077]

[0078]

[0079] Where d is the natural mortality rate of the predator population, and M(1) represents the maximum value of the random variable.

[0080] It is determined that these solutions are bounded. Assume that (x(t), y(t), u1(t), u2(t)) is a random model with arbitrary initial values Then for m ≥ 1, we have E[x m (t)]≤L(m) and E[y n (t)]≤M(n), where:

[0081]

[0082] Among them, E[x m (t)] represents the expectation of the random variable x(t) raised to the mth power, E[y n (t)] represents the expectation of the random variable y(t) to the nth power, x0 is the initial value of the random variable x(t), and y0 is the initial value of the random variable y(t).

[0083] Then, consider the conditions for the persistence of the population. Applying Ito's lemma to lnx(t) and lny(t), we can deduce:

[0084]

[0085] Among them, y(s) is the predator density at time s, x(s) is the prey density at time s, s is the integral variable, u1(s) is the prey control variable at time s, and u2(s) is the predator control variable at time s.

[0086] Applying the conditions Δ<0 and Δ0<0, and Lemma 2 in the reference [Meng Liu, Hong Qiu, Ke Wang, A remark on a stochastic predator-prey system with time delays, Applied Mathematics Letters, Volume 26, Issue 3, 2013, Pages 318-323, ISSN 0893-9659], we obtain:

[0087]

[0088] Therefore, (i) if Δ<0 and Δ0<0, all populations will become extinct.

[0089] Here, as stands for almost everywhere.

[0090] To obtain the conditions for partial population extinction, consider the following auxiliary system:

[0091]

[0092] According to Ito's formula and Lemma 2 in the reference [Meng Liu, Hong Qiu, Ke Wang, A remark on astochastic predator-prey system with time delays, Applied Mathematics Letters, Volume 26, Issue 3, 2013, Pages 318-323, ISSN 0893-9659], we have the following conclusions:

[0093]

[0094] in, represents the density of prey at time t in the auxiliary system, represents the density of predators in the auxiliary system at time t, B1(t) is the standard Brownian motion of the prey population at time t, B2(t) is the standard Brownian motion of the predator population at time t, and B1(s) is the standard Brownian motion of the prey population at time s.

[0095] Therefore, if Δ>0 and Δ1<0, populations x(t) and u1(t) will persist, while y(t) and u2(t) will become extinct.

[0096] Furthermore, in order to obtain conditions for the persistence of various populations.

[0097] according to If Δ>0 and Δ1>0, then it follows that:

[0098]

[0099] Then according to Δ2>0, we get:

[0100]

[0101] Therefore, according to the condition Δ3>0, we have:

[0102]

[0103] Therefore, populations x and y are persistent. In a similar way, we can get: if Δ>0, Δ i >0,i=1,2, then the control variables u1(t) and u2(t) are also persistent.

[0104] So for any initial value When t≥0, the solution of the random model (x(t), y(t), u1(t), u2(t)) satisfies the following properties:

[0105] (i) If Δ<0 and Δ0<0, then all populations will become extinct.

[0106] (ii) If Δ>0 and Δ1<0, then populations x(t) and u1(t) will persist, while y(t) and u2(t) will become extinct.

[0107] (iii) If Δ>0, and Δ i >0 for i=0,1,2, then all species x(t) and y(t) are permanent, while u1(t) and u2(t) are persistent.

[0108] In an optional embodiment, the constructing of a deterministic model of an ecosystem includes:

[0109] The deterministic model is constructed according to population information, fear levels, and refuge rates of various populations in the ecosystem, wherein the populations include prey and predators.

[0110] In an optional embodiment, the deterministic model is:

[0111]

[0112] Where x represents the prey density, x(t) represents the prey density at time t, y(t) represents the predator density, y(t) represents the predator density at time t, and u i (t)(i=1,2) represents the control variable. When i=1, u i (t) represents the control variable of the prey. When i=2, u i (t) represents the control variable of the predator; α is the intrinsic growth rate of the prey, b is the environmental carrying capacity of the prey, K represents the fear level, β represents the predator's ability to capture the prey, c is the conversion rate of the predator's prey, m represents the shelter rate, e is the first decay rate of the control variable, g is the second decay rate of the control variable, f represents the average effect of the prey on the disturbance rate, h represents the average effect of the predator on the disturbance rate, and n i (i=1,2) is the perturbation rate coefficient. When i=1, n i represents the disturbance rate coefficient experienced by the prey. When i = 2, n i represents the disturbance rate coefficient experienced by the predator, r is the predator population density constraint coefficient, and a is the half-saturation coefficient of the prey population.

[0113] In an alternative embodiment, see Figure 2 As shown, Figure 2 A flowchart of a random model construction method provided by the first embodiment of the present invention is shown, wherein the random model of the ecosystem is constructed based on the deterministic model, including steps S201 to S202:

[0114] S201: Define white noise in the complete probability space.

[0115] S202: The deterministic model constructs a stochastic model of the ecosystem, and the stochastic model is constructed according to the white noise and the noise intensity of the white noise.

[0116] Specifically, represents white noise, where B i (t) is a standard Brownian motion defined on the complete probability space (Ω, F, P). It satisfies the initial conditions B1(0) = 0, B2(0) = 0, σ i (i=1,2) represents the standard deviation of white noise, where is the intensity of the white noise.

[0117] Embodiment 2

[0118] See also Figure 3 As shown, Figure 3The schematic diagram of the structure of an ecosystem dynamic characteristics analysis device provided by the second embodiment of the present invention is shown, wherein the device comprises:

[0119] An ecosystem model construction module 301 is used to construct a deterministic model of an ecosystem, and to construct a stochastic model of the ecosystem based on the deterministic model, wherein the deterministic model includes several key variables in the ecosystem;

[0120] The dynamic characteristic definition module 302 is used to define the global asymptotic stability of the deterministic model, the existence of the global correct solution of the stochastic model, and the population persistence of the ecosystem, and determine the value relationship between the key variables of the ecosystem when the global asymptotic stability, the existence of the global correct solution, and the population persistence are satisfied;

[0121] The dynamic characteristic analysis module 303 is used to perform numerical simulation on the stochastic model based on the value relationship between each key variable to analyze the dynamic characteristics of the ecosystem.

[0122] In an optional embodiment, the constructing of a deterministic model of an ecosystem includes:

[0123] The deterministic model is constructed according to population information, fear levels, and refuge rates of various populations in the ecosystem, wherein the populations include prey and predators.

[0124] In an optional embodiment, the deterministic model is:

[0125]

[0126] Where x represents the prey density, x(t) represents the prey density at time t, y(t) represents the predator density, y(t) represents the predator density at time t, and u i (t)(i=1,2) represents the control variable. When i=1, u i (t) represents the control variable of the prey. When i=2, u i (t) represents the control variable of the predator; α is the intrinsic growth rate of the prey, b is the environmental carrying capacity of the prey, K represents the fear level, β represents the predator's ability to capture the prey, c is the conversion rate of the predator's prey, m represents the shelter rate, e is the first decay rate of the control variable, g is the second decay rate of the control variable, f represents the average effect of the prey on the disturbance rate, h represents the average effect of the predator on the disturbance rate, and n i (i=1,2) is the perturbation rate coefficient. When i=1, n i represents the disturbance rate coefficient experienced by the prey. When i = 2, n irepresents the disturbance rate coefficient experienced by the predator, r is the predator population density constraint coefficient, and a is the half-saturation coefficient of the prey population.

[0127] In an optional embodiment, constructing the stochastic model of the ecosystem based on the deterministic model comprises:

[0128] White noise defined in complete probability space;

[0129] The deterministic model constructs a stochastic model of the ecosystem, and the stochastic model is constructed according to the white noise and the noise intensity of the white noise.

[0130] The ecosystem dynamic characteristics analysis device provided in the embodiment of the present invention can be specific hardware on the device or software or firmware installed on the device. The implementation principle and technical effects of the device provided in the embodiment of the present invention are the same as those of the aforementioned method embodiment. For the sake of brief description, the parts not mentioned in the device embodiment can refer to the corresponding contents in the aforementioned method embodiment. Technical personnel in the relevant field can clearly understand that for the convenience and simplicity of description, the specific working processes of the systems, devices and units described above can all refer to the corresponding processes in the aforementioned method embodiment, and will not be repeated here.

[0131] In the embodiments provided by the present invention, it should be understood that the disclosed devices and methods can be implemented in other ways. The device embodiments described above are only schematic. For example, the division of the units is only a logical function division. There may be other division methods in actual implementation. For example, multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the mutual coupling or direct coupling or communication connection shown or discussed can be through some communication interfaces, and the indirect coupling or communication connection of devices or units can be electrical, mechanical or other forms.

[0132] The units described as separate components may or may not be physically separated, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed on multiple network units. Some or all of the units may be selected according to actual needs to achieve the purpose of the solution of this embodiment.

[0133] In addition, each functional unit in the embodiment provided by the present invention may be integrated into one processing unit, or each unit may exist physically separately, or two or more units may be integrated into one unit.

[0134] If the functions are implemented in the form of software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art or the part of the technical solution, can be embodied in the form of a software product. The computer software product is stored in a storage medium, including several instructions for a computer device (which can be a personal computer, a server, or a network device, etc.) to perform all or part of the steps of the methods described in each embodiment of the present invention. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), disk or optical disk, etc., which can store program codes.

[0135] It should be noted that similar numbers and letters represent similar items in the following figures. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures. In addition, the terms "first", "second", "third", etc. are only used to distinguish the description and are not to be understood as indicating or implying relative importance.

[0136] Finally, it should be noted that the above-described embodiments are only specific implementations of the present invention, which are used to illustrate the technical solutions of the present invention, rather than to limit them. The protection scope of the present invention is not limited thereto. Although the present invention is described in detail with reference to the above-described embodiments, those skilled in the art should understand that any person skilled in the art can still modify the technical solutions described in the above-described embodiments within the technical scope disclosed by the present invention, or can easily think of changes, or perform equivalent replacements on some of the technical features thereof; and these modifications, changes or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present invention. They should all be covered within the protection scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims

1. A method for analyzing dynamic characteristics of an ecosystem, characterized in that: The method comprises: Constructing a deterministic model of an ecosystem, and constructing a stochastic model of the ecosystem based on the deterministic model, wherein the deterministic model includes several key variables in the ecosystem; The global asymptotic stability of the deterministic model, the existence of global positive solutions of the stochastic model, and the population persistence of the ecosystem are defined respectively; The value relationship between the key variables of the ecosystem when satisfying the global asymptotic stability, the existence of the global correct solution and the population persistence is determined to realize the dynamic characteristic analysis of the ecosystem.

2. The method according to claim 1, characterized in that The deterministic model for building an ecosystem includes: The deterministic model is constructed according to population information, fear levels, and refuge rates of various populations in the ecosystem, wherein the populations include prey and predators.

3. The method according to claim 1, characterized in that The deterministic model is: Where x represents the prey density, x(t) represents the prey density at time t, y(t) represents the predator density, y(t) represents the predator density at time t, and u i (t)(i=1,2) represents the control variable. When i=1, u i (t) represents the control variable of the prey. When i = 2, u i (t) represents the control variable of the predator; α is the intrinsic growth rate of the prey, b is the environmental carrying capacity of the prey, K represents the fear level, β represents the predator's ability to capture the prey, c is the conversion rate of the predator's prey, m represents the shelter rate, e is the first decay rate of the control variable, g is the second decay rate of the control variable, f represents the average effect of the prey on the disturbance rate, h represents the average effect of the predator on the disturbance rate, and n i (i=1,2) is the perturbation rate coefficient. When i=1, n i represents the disturbance rate coefficient experienced by the prey. When i = 2, n i represents the disturbance rate coefficient experienced by the predator, r is the predator population density constraint coefficient, and a is the half-saturation coefficient of the prey population.

4. The method according to claim 1, characterized in that The step of constructing the stochastic model of the ecosystem based on the deterministic model comprises: White noise defined in the complete probability space; The deterministic model constructs a stochastic model of the ecosystem, and the stochastic model is constructed according to the white noise and the noise intensity of the white noise.

5. An ecosystem dynamic characteristics analysis device, characterized in that: The device comprises: An ecosystem model construction module, used to construct a deterministic model of the ecosystem, and to construct a stochastic model of the ecosystem based on the deterministic model, wherein the deterministic model includes several key variables in the ecosystem; A dynamic characteristic definition module, used to define the global asymptotic stability of the deterministic model, the existence of global positive solutions of the stochastic model, and the population persistence of the ecosystem; The dynamic characteristic analysis module is used to determine the value relationship between key variables when the ecosystem satisfies the global asymptotic stability, the existence of the global correct solution and the population persistence, so as to realize the dynamic characteristic analysis of the ecosystem.

6. The device according to claim 5, characterized in that The deterministic model for building an ecosystem includes: The deterministic model is constructed according to population information, fear levels, and refuge rates of various populations in the ecosystem, wherein the populations include prey and predators.

7. The device according to claim 5, characterized in that The deterministic model is: Where x represents the prey density, x(t) represents the prey density at time t, y(t) represents the predator density, y(t) represents the predator density at time t, and u i (t)(i=1,2) represents the control variable. When i=1, u i (t) represents the control variable of the prey. When i = 2, u i (t) represents the control variable of the predator; α is the intrinsic growth rate of the prey, b is the environmental carrying capacity of the prey, K represents the fear level, β represents the predator's ability to capture the prey, c is the conversion rate of the predator's prey, m represents the shelter rate, e is the first decay rate of the control variable, g is the second decay rate of the control variable, f represents the average effect of the prey on the disturbance rate, h represents the average effect of the predator on the disturbance rate, and n i (i=1,2) is the perturbation rate coefficient. When i=1, n i represents the disturbance rate coefficient experienced by the prey. When i = 2, n i represents the disturbance rate coefficient experienced by the predator, r is the predator population density constraint coefficient, and a is the half-saturation coefficient of the prey population.

8. The device according to claim 5, characterized in that The step of constructing the stochastic model of the ecosystem based on the deterministic model comprises: White noise defined in the complete probability space; The deterministic model constructs a stochastic model of the ecosystem, and the stochastic model is constructed according to the white noise and the noise intensity of the white noise.

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