A method and device for analyzing the dynamic characteristics of an ecosystem

Abstract

The present application provides a method and device for analyzing the dynamic characteristics of an ecosystem. Specifically, a deterministic model of the ecosystem is constructed, and a stochastic model of the ecosystem is constructed based on the deterministic model, where the deterministic model includes several key variables in the ecosystem; the global asymptotic stability of the deterministic model, the existence of a global positive solution of the stochastic model, and the population persistence of the ecosystem are respectively defined, and the value relationship between the key variables when the ecosystem satisfies the global asymptotic stability, the global positive solution existence, and the population persistence is determined, so as to realize the analysis of the dynamic characteristics of the ecosystem. By using the above method, an accurate, effective and comprehensive analysis of the dynamic characteristics of the ecosystem can be realized.

Description

Technical Field

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

[0002] With the deep intervention of human activities in natural ecosystems, the interactions between species in ecosystems have become increasingly complex, especially the relationship between prey and predators. Although traditional prey-predator models provide us with a certain theoretical basis, their explanatory and predictive capabilities are limited when faced with complex interactions in real ecosystems. First, the fear effect is an important factor that cannot be ignored in ecosystems. When prey encounters a predator, it often generates a sense of fear, which not only affects the behavior of the prey but also indirectly affects the stability of the entire ecosystem. However, traditional models often ignore this important factor. Second, prey refuges widely exist in real ecosystems. When prey faces predator pressure, it will seek refuges to avoid being chased by predators. The existence of such refuges has an important impact on the stability of the ecosystem and the species coexistence mechanism, but traditional models often fail to fully consider it. Finally, feedback control is a basic mechanism in ecosystems. The various components in an ecosystem maintain the stability and balance of the ecosystem through mutual interaction and feedback regulation. However, traditional models often simplify or ignore this mechanism when describing it. It can be seen that the existing prey-predator models cannot accurately, effectively, and comprehensively analyze the dynamic characteristics of ecosystems. Therefore, how to accurately, effectively, and comprehensively analyze the dynamic characteristics of ecosystems has become an urgent problem to be solved. Summary of the Invention

[0003] In view of this, the purpose of the present invention is to provide a method and device for analyzing the dynamic characteristics of an ecosystem 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 the dynamic characteristics of an ecosystem, the method including:

[0005] Construct a deterministic model of the ecosystem and construct a stochastic model of the ecosystem based on the deterministic model, where the deterministic model includes several key variables in the ecosystem;

[0006] Define 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 respectively;

[0007] Determine the value relationship between the key variables of the ecosystem when satisfying the global asymptotic stability, the existence of the global positive solution, and the population persistence, so as to realize the dynamic characteristic analysis of the ecosystem.

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

[0009] Construct the deterministic model according to the population information, fear level, and shelter rate of various populations in the ecosystem, where the populations include prey and predators.

[0010] Optionally, the deterministic model is:

[0011]

[0012] Among them, x represents the prey density, x(t) represents the prey density at time t, y(t) represents the predator density, \(\dot{y}(t)\) represents the predator density at time t, \(u_i(t)(i = 1, 2)\) represents the control variable. When \(i = 1\), \(u_1(t)\) represents the control variable of the prey. When \(i = 2\), \(u_2(t)\) represents the control variable of the predator; \(\alpha\) is the intrinsic growth rate of the prey, b is the environmental carrying capacity of the prey, K represents the fear level, \(\beta\) represents the capture ability of the predator to the prey, c is the conversion rate of the predator preying on the 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 impact of the prey on the interference rate, h represents the average impact of the predator on the interference rate, \(n_i(i = 1, 2)\) is the disturbance rate coefficient. When \(i = 1\), \(n_1\) represents the disturbance rate coefficient experienced by the prey. When \(i = 2\), \(n_2\) represents the disturbance rate coefficient experienced by the predator, r is the predator population density restriction coefficient, and a is the half-saturation coefficient of the prey population. i \(\dot{x}(t)=\alpha x(t)(1-\frac{x(t)}{b})-\frac{\beta x(t)y(t)}{1+\frac{x(t)}{a}}+u_1(t)-n_1x(t)+fx(t)\sum_{j = 1}^{m}\xi_j(t)\) i \(\dot{y}(t)=-\gamma y(t)+\frac{\beta cx(t)y(t)}{1+\frac{x(t)}{a}}+u_2(t)-n_2y(t)+hy(t)\sum_{j = 1}^{m}\xi_j(t)\) i i i i

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

[0014] Define white noise in a complete probability space;

[0015] Construct the stochastic model of the ecosystem from the deterministic model, and construct the stochastic model 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 apparatus for analyzing the dynamic characteristics of an ecosystem. The apparatus includes:

[0017] An ecosystem model construction module, which is used to construct a deterministic model of the ecosystem and 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, which is used to define 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 respectively;

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

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

[0021] Constructing the deterministic model according to the population information, fear level, and shelter rate of various populations in the ecosystem, where 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, 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 capture ability of the predator for the prey, c is the conversion rate of the predator preying on the 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 impact of the prey on the interference rate, h represents the average impact of the predator on the interference rate, n i (i = 1, 2) is the perturbation rate coefficient. When i = 1, n i represents the perturbation rate coefficient experienced by the prey. When i = 2, n i represents the perturbation rate coefficient experienced by the predator, r is the predator population density restriction 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] Defining white noise in a complete probability space;

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

[0028] The technical solutions provided in this application include but are not limited to the following beneficial effects:

[0029] This application constructs a deterministic model of the ecosystem and constructs a stochastic model of the ecosystem based on the deterministic model. Among them, the deterministic model includes several key variables in the ecosystem, which can comprehensively consider the impacts of multiple factors such as fear effects, prey refuges, and feedback control on the ecosystem, making the model 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 relationships between the key variables are determined when the ecosystem satisfies the global asymptotic stability, the global positive solution existence, and the population persistence. It can apply the model to multiple fields such as ecosystem stability assessment, species coexistence mechanism research, and ecological restoration and reconstruction, providing practical tools and methods for the management and protection of the ecosystem. Since the model has a powerful multi-scenario simulation ability, it can simulate the dynamic change process of the ecosystem under different scenarios. This ability makes the model more flexible and practical when dealing with different ecological environment problems and formulating management strategies. At the same time, variables such as fear effects, prey refuges, and feedback control in the model simulate their actual effects through refined parameter settings. 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 value relationships between the key variables are determined when the ecosystem satisfies the global asymptotic stability, the global positive solution existence, and the population persistence, so as to realize the analysis of the dynamic characteristics of the ecosystem. The value relationships between the key variables are determined when the ecosystem satisfies the global asymptotic stability, the global positive solution existence, and the population persistence, so as to realize an accurate, effective, and comprehensive analysis of the dynamic characteristics of the ecosystem.

[0030] To make the above objects, features, and advantages of the present invention more obvious and understandable, the following preferred embodiments are specifically described below in conjunction with the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as limiting the scope. For those of ordinary skill in the art, other related drawings can be obtained based on these drawings without creative efforts.

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

[0033] Figure 2 The flowchart of a method for constructing a stochastic model provided by Embodiment 1 of the present invention is shown;

[0034] Figure 3 The structural schematic diagram of a device for analyzing the dynamic characteristics of an ecosystem provided by Embodiment 2 of the present invention is shown. Detailed implementation manners

[0035] To make the objectives, 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 with reference to the accompanying drawings in the embodiments of the present invention. Apparently, the described embodiments are only a part rather than all of the embodiments of the present invention. Usually, the components of the embodiments of the present invention described and illustrated in the accompanying 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 accompanying drawings is not intended to limit the scope of the claimed present 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 creative efforts fall within the scope of protection of the present invention.

[0036] Embodiment 1

[0037] Explanation of relevant terms in this application:

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

[0039] 2. Prey refuge: A safe area or resource that a prey population can utilize when facing predator pressure to reduce the risk of being preyed upon. Such a refuge usually refers to a place where the prey can hide or protect itself, such as a concealed habitat, an area that cannot be easily approached by a predator, or a place with specific protection measures. In a mathematical model, a prey refuge can be modeled as an additional parameter or function to describe the probability or effect of the prey choosing to use the refuge, as well as the impact of this choice on the predator-prey dynamics. Increasing the number or effectiveness of prey refuges usually reduces 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 regulating the environment or behavior. This control strategy can influence the interactions between populations and overall stability by changing population density or other biological characteristics. In a predator-prey model, feedback control can affect the dynamic balance between predators and prey by adjusting the relative numbers, predation rates, reproduction rates, etc. between them. This control strategy can help maintain the stability of the ecosystem and prevent problems such as overpredation or over-reproduction.

[0041] 4. Global asymptotic stability: It means that after a period of time, regardless of the initial conditions, 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 Signs is a mathematical tool used to analyze the number of positive and negative roots of a high-degree polynomial.

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

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

[0045] 8. Local Lipschitz continuity: When solving differential equations, it ensures the existence and uniqueness of solutions.

[0046] 9. The basic idea of Itô's formula is to generalize the chain rule, product rule, integral rule, etc. in calculus to stochastic processes. Through Itô's lemma, the differential components such as the derivative and integral of a stochastic process can be calculated, so as to more deeply understand the evolution law of the stochastic process.

[0047] For the convenience of understanding this application, the following will combine Figure 1 the content described in the flowchart of a method for analyzing the dynamic characteristics of an ecosystem provided by Embodiment 1 of the present invention shown below to describe Embodiment 1 of this application in detail.

[0048] See Figure 1 as shown Figure 1The flowchart of an ecosystem dynamic characteristic analysis method provided by Embodiment 1 of the present invention is shown, wherein the method includes steps S101 to S103:

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

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

[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, 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 capture ability of the predator on the prey, c is the conversion rate of the predator preying on the 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 impact of the prey on the interference rate, h represents the average impact of the predator on the interference rate, n i (i = 1, 2) is the disturbance 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 restriction coefficient, and a is the half-saturation coefficient of the prey population.

[0053] Define white noise to simulate the environmental disturbance in the ecosystem, and construct a stochastic model of the ecosystem based on the above deterministic model on the basis of white noise. The stochastic model is specifically:

[0054]

[0055] where, represents white noise. When i = 1, represents the white noise impact on the prey population. When i = 2, represents the white noise impact on the predator population, B i (t) is a standard Brownian motion defined on the complete probability space (Ω, F, P). Satisfy 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 white noise received by the prey population. When i = 2, σ i represents the standard deviation of white noise received by the predator population, where is the intensity of white noise.

[0056] S102: Define 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 respectively.

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

[0058] Specifically, next, analyze and prove the global asymptotic stability, the existence of the global positive solution of the stochastic model, and the population persistence of the ecosystem.

[0059] First, define the positivity of the equilibrium point and the global asymptotic stability of the interior equilibrium point for the deterministic model. The boundary equilibrium points of the deterministic model are:

[0060]

[0061] The interior equilibrium point of the deterministic model is where x * is the value of the prey population in the interior equilibrium point, y * is the value of the predator population in the interior equilibrium point, is the value of the feedback control variable received by the prey population, is the value of the feedback control variable received by the predator population, and d is the mortality rate of the predator.

[0062] According to Descartes′ Rule of Signs, the uniqueness of the interior equilibrium point is obtained. To prove the global asymptotic stability of the unique interior equilibrium point, the Lyapunov function is introduced to judge the asymptotic stability of the interior equilibrium point. The specific function V(t) is:

[0063]

[0064] where p i , q i (i = 1, 2) are positive constants; when i = 1, p i represents the coefficient of the prey term in the constructed Lyapunov function, q idenotes the coefficient of the prey in the constructed Lyapunov function with respect to the feedback control variable term; when \(i = 2\), \(p\) i denotes the coefficient of the predator in the constructed Lyapunov function, \(q\) i denotes the coefficient of the predator in the constructed Lyapunov function with respect to the feedback control variable term; through calculation, and by using the existence and uniqueness of the interior equilibrium point and the Lyapunov asymptotic stability theorem, the global asymptotic stability of the interior equilibrium point \(E\) * can be obtained, where \(u_1\) is the control variable of the prey and \(u_2\) is the control variable of the predator.

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

[0066] Since the coefficients of the stochastic model satisfy local Lipschitz continuity, on the interval \([0,\tau\) e , there exists a unique local positive solution \((x(t),y(t),u_1(t),u_2(t))\). To deduce the global nature of this solution, it is necessary to prove that the explosion time \(\tau\) e =\(\infty\) almost surely (a.s.). Without loss of generality, define the stopping time \(\tau\) k :

[0067]

[0068] or \(\max\{x(t),y(t),u_1(t),u_2(t)\}\geq k\);

[0069] where \(k\) is a constant, and \(x(t),y(t),u_1(t),u_2(t)\) represent the densities of the prey, predator, the feedback control variable received by the prey, and the feedback control variable received by the predator in the system at time \(t\), respectively.

[0070] Then, \(\tau\) k increases as \(k\rightarrow\infty\). Let Obviously, \(\tau\) ∞ \(\leq\tau\) e . Now, it is necessary to prove that \(\tau\) ∞ =\(\infty\) almost surely. Using the proof by contradiction, assume that \(\tau\) ∞ =\(\infty\) does not hold, and construct a suitable Lyapunov function: \(\tau\) ∞ is the limit of the stopping time \(\tau\) k as \(k\rightarrow+\infty\).

[0071] Using Itô's formula, we can obtain: Let \(k\rightarrow\infty\), then a contradiction is obtained. Thus, the existence of the global positive solution of the stochastic model is proved. \(x(0)\), \(y(0)\), \(u_1(0)\), \(u_2(0)\) represent the initial values of the prey, predator, the feedback control variable received by the prey, and the feedback control variable received by the predator in the system, respectively.

[0072] Next, consider discussing the asymptotics of the stochastic model at the interior equilibrium point of the deterministic model.

[0073] Suppose \((x(t),y(t),u_1(t),u_2(t))\) is the solution of the stochastic model with arbitrary initial value . If the following conditions are satisfied: and then this solution has the following properties:

[0074]

[0075] where, represents the 4 - dimensional positive real number space, \(E\) represents the expectation, and \(\theta\) represents an arbitrarily - valued parameter.

[0076] Immediately, define the persistence criterion of the stochastic model, which is a key step in controlling the stability of the ecosystem. First, 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 obtained by the random variable.

[0080] It is determined that these solutions are bounded. Suppose \((x(t),y(t),u_1(t),u_2(t))\) is the solution of the stochastic model with arbitrary initial value . Then for \(m\geq1\), we have \(E[x^{ m}](t)]\leq L(m)\) and \(E[y^{ n}](t)]\leq M(n)\), where:

[0081]

[0082] where, \(E[x^{ m}](t)\) represents the expectation of the \(m\) - th power of the random variable \(x(t)\), \(E[y^{ n}](t)\) represents the expectation of the \(n\) - th power of the random variable \(y(t)\), \(x_0\) is the initial value of the random variable \(x(t)\), and \(y_0\) is the initial value of the random variable \(y(t)\).

[0083] Then, consider the conditions for the persistence of the population. Applying Itô's lemma to \(\ln x(t)\) and \(\ln y(t)\), we can deduce that:​

[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 integration variable, \(u_1(s)\) is the prey control variable at time \(s\), and \(u_2(s)\) is the predator control variable at time \(s\).

[0086] Applying the conditions \(\Delta\lt0\) and \(\Delta_0\lt0\), 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 get:

[0087]

[0088] Therefore, (i) if \(\Delta\lt0\) and \(\Delta_0\lt0\), then all populations will go extinct.

[0089] Among them, a.s. represents almost everywhere.

[0090] To obtain the conditions for the extinction of some populations, consider the following auxiliary system:

[0091]

[0092] According to Itô's formula 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 have the following conclusion:

[0093]

[0094] Among them, represents the prey density at time \(t\) in the auxiliary system, represents the predator density at time \(t\) in the auxiliary system, \(B_1(t)\) is the standard Brownian motion suffered by the prey population at time \(t\), \(B_2(t)\) is the standard Brownian motion suffered by the predator population at time \(t\), and \(B_1(s)\) is the standard Brownian motion suffered by the prey population at time \(s\).

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

[0096] Furthermore, to obtain the conditions for all populations to persist.

[0097] According to If Δ > 0 and Δ1 > 0, then it is deduced that:

[0098]

[0099] Then, according to Δ2 > 0, it is obtained that:

[0100]

[0101] Therefore, according to the condition Δ3 > 0, there is:

[0102]

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

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

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

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

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

[0108] In an alternative embodiment, the construction of the deterministic model of the ecosystem includes:

[0109] Construct the deterministic model according to the population information, fear level, and shelter rate of various populations in the ecosystem, where the populations include prey and predators.

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

[0111]

[0112] Among them, 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 capture ability of the predator for the prey, c is the conversion rate of the predator preying on the 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 impact of the prey on the interference rate, h represents the average impact of the predator on the interference rate, and n i (i = 1, 2) is the disturbance 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 restriction coefficient, and a is the half-saturation coefficient of the prey population.

[0113] In an alternative embodiment, see Figure 2 as shown in Figure 2 shows a flowchart of a method for constructing a stochastic model provided in Embodiment 1 of the present invention. Among them, constructing the stochastic model of the ecosystem based on the deterministic model includes steps S201 to S202:

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

[0115] S202: The deterministic model constructs the stochastic model of the ecosystem, and constructs the stochastic model 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 a complete probability space (Ω, F, P). Satisfying the initial conditions B1(0) = 0, B2(0) = 0, σ i (i = 1, 2) represents the standard deviation of the white noise, where is the intensity of the white noise.

[0117] Embodiment 2

[0118] See Figure 3 as shown in Figure 3The following shows a schematic structural diagram of an ecological system dynamic characteristic analysis device provided in the second embodiment of the present invention. Among them, the device includes:

[0119] An ecological system model construction module 301, configured to construct a deterministic model of the ecological system, and construct a stochastic model of the ecological system based on the deterministic model, where the deterministic model includes several key variables in the ecological system;

[0120] A dynamic characteristic definition module 302, configured to respectively define the global asymptotic stability of the deterministic model, the existence of a global positive solution of the stochastic model, and the population persistence of the ecological system, and determine the value relationship between each key variable when the ecological system satisfies the global asymptotic stability, the global positive solution existence, and the population persistence;

[0121] A dynamic characteristic analysis module 303, configured to perform numerical simulation on the stochastic model based on the value relationship between each key variable to analyze the dynamic characteristics of the ecological system.

[0122] In an optional implementation manner, constructing the deterministic model of the ecological system includes:

[0123] Constructing the deterministic model according to the population information, fear level, and shelter rate of various populations in the ecological system, where the populations include prey and predators.

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

[0125]

[0126] Among them, x represents the prey density, x(t) represents the prey density at time t, y(t) represents the predator density, \(\dot{y}(t)\) represents the predator density at time t, \(u_i(t)\) (\(i = 1, 2\)) represents the control variable. When \(i = 1\), \(u_1(t)\) represents the control variable of the prey. When \(i = 2\), \(u_2(t)\) represents the control variable of the predator; \(\alpha\) is the intrinsic growth rate of the prey, b is the environmental carrying capacity of the prey, K represents the fear level, \(\beta\) represents the capture ability of the predator for the prey, c is the conversion rate of the predator preying on the 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 influence of the prey on the interference rate, h represents the average influence of the predator on the interference rate, \(n_i\) (\(i = 1, 2\)) is the perturbation rate coefficient. When \(i = 1\), \(n_1\) represents the perturbation rate coefficient experienced by the prey. When \(i = 2\), \(n_2\) 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 capture ability of the predator for the prey, c is the conversion rate of the predator preying on the 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 influence of the prey on the interference rate, h represents the average influence of the predator on the interference rate, n i (i=1,2) is the perturbation rate coefficient. When i=1, n i represents the perturbation rate coefficient experienced by the prey. When i=2, n irepresents the disturbance rate coefficient experienced by the predator, r is the density-dependent coefficient of the predator population, and a is the half-saturation coefficient of the prey population.

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

[0128] Defining white noise in a complete probability space;

[0129] Constructing the stochastic model of the ecosystem by the deterministic model, and constructing the stochastic model according to the white noise and the noise intensity of the white noise.

[0130] The device for analyzing the dynamic characteristics of the ecosystem provided by the embodiments of the present invention may be specific hardware on the device or software or firmware installed on the device, etc. The implementation principle and the technical effects generated by the device provided by the embodiments of the present invention are the same as those of the foregoing method embodiments. For the sake of brief description, for the parts not mentioned in the device embodiments, reference may be made to the corresponding content in the foregoing method embodiments. Those skilled in the art 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 foregoing method embodiments, 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 merely illustrative. For example, the division of the units is only a logical function division, and there may be other division methods in actual implementation. For another 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 displayed or discussed couplings or direct couplings or communication connections to each other can be through some communication interfaces. The indirect couplings or communication connections of the devices or units can be electrical, mechanical, or other forms.

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

[0133] In addition, the functional units in the embodiments provided by the present invention can be integrated into one processing unit, or each unit exists physically alone, or two or more units can be integrated into one unit.

[0134] When the above-mentioned 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, in essence, or the part that contributes to the prior art or a part of this technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions for causing a computer device (which may be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the methods described in various embodiments of the present invention. The aforementioned storage medium includes: various media such as USB flash drives, mobile hard disks, read-only memories (ROM, Read-Only Memory), random access memories (RAM, Random Access Memory), magnetic disks, or optical discs that can store program codes.

[0135] It should be noted that: similar reference numerals and letters represent similar items in the following drawings. Therefore, once an item is defined in one drawing, it does not need to be further defined and explained in subsequent drawings. In addition, the terms "first", "second", "third", etc. are only used for descriptive distinction and cannot be understood as indicating or implying relative importance.

[0136] Finally, it should be noted that: the above-mentioned embodiments are only specific implementation manners of the present invention, used to illustrate the technical solutions of the present invention, rather than limiting it. The protection scope of the present invention is not limited thereto. Although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that: any person skilled in the art within the technical scope disclosed by the present invention can still modify the technical solutions described in the foregoing embodiments, or can easily think of changes, or make equivalent replacements for some of the technical features; 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. All should be covered within the protection scope of the present invention. Therefore, the protection scope of the present invention should 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; Determine the value relationship between key variables of the ecosystem when the ecosystem satisfies the global asymptotic stability, the existence of the global positive solution and the persistence of the population, so as to realize the dynamic characteristic analysis of the ecosystem; 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) represents the control variable, i=1,2, 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 is the disturbance rate coefficient, i=1,2, 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.

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 step of constructing the stochastic model of the ecosystem based on the deterministic model comprises: White noise defined in 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.

4. 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; A dynamic characteristic analysis module, used to determine the value relationship between key variables of the ecosystem when the ecosystem satisfies the global asymptotic stability, the existence of the global positive solution and the persistence of the population, so as to realize the dynamic characteristic analysis of the ecosystem; 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) represents the control variable, i=1,2, 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 is the disturbance rate coefficient, i=1,2, 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.

5. The device according to claim 4, 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.

6. The device according to claim 4, characterized in that The step of constructing the stochastic model of the ecosystem based on the deterministic model comprises: White noise defined in 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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