A predator-prey model with prey dispersal and Holling type-Ⅱ functional response is investigated.In this model,the time delay due to the gestation of the predator and stagestructure for the predator are considered.By...A predator-prey model with prey dispersal and Holling type-Ⅱ functional response is investigated.In this model,the time delay due to the gestation of the predator and stagestructure for the predator are considered.By analyzing the corresponding characteristic equations,the local stability of each of the nonnegative equilibria is discussed.The existence of Hopf bifurcations at the positive equilibrium is established.By using Lyapunov functionals and LaSalle’s invariance principle,sufficient conditions are obtained for the global stability of the positive equilibrium,the nonnegative boundary equilibrium and the trivial equilibrium of the model,respectively.Numerical simulations are carried out to illustrate the main results.展开更多
This paper examines an epidemic predator-prey model with prey dispersal and Holling type-II functional response. In this model, it is assumed that the predator population suffers a transmissible disease. By analyzing ...This paper examines an epidemic predator-prey model with prey dispersal and Holling type-II functional response. In this model, it is assumed that the predator population suffers a transmissible disease. By analyzing the corresponding characteristic equations, the local stability of each of feasible equilibria and the existence of Hopf bifurcations at the coexistence equilibrium is addressed. Using Lyapunov functionals and LaSalle's invariance principle, we obtained the sufficient conditions for the global stability of the trivial equilibrium, the predator-extinction equilibrium, the disease-free equilibrium and the coexistence equilibrium, respectively. The paper also includes numerical simulations to illustrate the analytical results.展开更多
This paper investigates the number of limit cycles in a predator-prey system with group defense,intially introduced by Wolkowicz and later examined by Rothe and Shafer in the 1980’s.Under the assumption of large prey...This paper investigates the number of limit cycles in a predator-prey system with group defense,intially introduced by Wolkowicz and later examined by Rothe and Shafer in the 1980’s.Under the assumption of large prey growth,the system reduces to a perturbed singular system,whose limit cycles can be analyzed using geometric singular perturbation methods-primarily through the study of a slow-divergence integral.Our work completes partially the results previously obtained by Li and Zhu and by Hsu.We provide a comprehensive classification of all possible singular cycles capable of generating limit cycles and analyze the slow-divergence integral for the nine distinct types of cycle families that arise in a canard explosion.Based on these findings,we demonstrate that the maximum number of limit cycles emerging from the singular cycles is two in all cases,thereby confirming conjectures posed by Rothe-Shafer and Xiao-Ruan.展开更多
One of the main objectives of artificial intelligence lies in the simulation of the behavior of living organisms;emotions are a fundamental part of life, and they cannot be left aside when simulating behavior. In this...One of the main objectives of artificial intelligence lies in the simulation of the behavior of living organisms;emotions are a fundamental part of life, and they cannot be left aside when simulating behavior. In this research, software is developed that simulates the behavior of birds with different characteristics. The latter interacts by considering different stimuli from the environment (external), and the internal state of the subject (objectives). To achieve this, a model of birds in the role of prey and predators is developed that focuses on the study of the interaction between these organisms that exhibit specific behaviors in their environment. This project is a seminal work that aims to represent the emotions of birds, and the latter caused by stimuli from a dynamic environment.展开更多
Subject to the homogeneous Neumann boundary condition, a ratio-dependent predator-prey reaction diffusion model is discussed. An improved result for the model is derived, that is, the unique positive constant steady s...Subject to the homogeneous Neumann boundary condition, a ratio-dependent predator-prey reaction diffusion model is discussed. An improved result for the model is derived, that is, the unique positive constant steady state is the global stability. This is done using the comparison principle and establishing iteration schemes involving positive solutions supremum and infimum. The result indicates that the two species will ultimately distribute homogeneously in space. In fact, the comparison argument and iteration technique to be used in this paper can be applied to some other models. This method deals with the not-existence of a non-constant positive steady state for some reaction diffusion systems, which is rather simple but sufficiently effective.展开更多
This article is focusing on a class of multi-delay predator-prey model with feedback controls and prey diffusion. By developing some new analysis methods and using the theory of differential inequalities as well as co...This article is focusing on a class of multi-delay predator-prey model with feedback controls and prey diffusion. By developing some new analysis methods and using the theory of differential inequalities as well as constructing a suitable Lyapunov function, we establish a set of easily verifiable sufficient conditions which guarantee the permanence of the system and the globally attractivity of positive solution for the predator-prey system.Furthermore, some conditions for the existence, uniqueness and stability of positive periodic solution for the corresponding periodic system are obtained by using the fixed point theory and some new analysis techniques. In additional, some numerical solutions of the equations describing the system are given to verify the obtained criteria are new, general, and easily verifiable. Finally, we still solve numerically the corresponding stochastic predator-prey models with multiplicative noise sources, and obtain some new interesting dynamical behaviors of the system.展开更多
The nonlinear predator-prey reaction diffusion systems for singularly perturbed Robin Problems are considered. Under suitable conditions, the theory of differential inequalities can be used to study the asymptotic beh...The nonlinear predator-prey reaction diffusion systems for singularly perturbed Robin Problems are considered. Under suitable conditions, the theory of differential inequalities can be used to study the asymptotic behavior of the solution for initial boundary value problems.展开更多
This paper deals with the global dynamical behaviors of the positive solutions for a parabolic type ratio-dependent predator-prey system with a crowding term in the prey equation, where it is assumed that the coeffici...This paper deals with the global dynamical behaviors of the positive solutions for a parabolic type ratio-dependent predator-prey system with a crowding term in the prey equation, where it is assumed that the coefficient of the functional response is less than the coefficient of the intrinsic growth rates of the prey species. We demonstrated some special dynamical behaviors of the positive solutions of this system which the persistence of the coexistence of two species can be obtained when the crowding region in the prey equation only is designed suitably. Furthermore, we can obtain that under some conditions, the unique positive steady state solution of the system is globally asymptotically stable.展开更多
An actual ecological predator-prey system often undergoes random environmental mutations owing to the impact of natural disasters and man-made destruction, which may destroy the balance between the species. In this pa...An actual ecological predator-prey system often undergoes random environmental mutations owing to the impact of natural disasters and man-made destruction, which may destroy the balance between the species. In this paper,the stochastic dynamics of the nonlinear predator-prey system considering random environmental mutations is investigated, and a feedback control strategy is proposed to reshape the response of the predator-prey system against random abrupt environmental mutations. A delayed Markov jump system(MJS) is established to model such a predator-prey system. A novel first integral is constructed which leads to better approximation solutions of the ecosystem. Then, by applying the stochastic averaging method based on this novel first integral, the stochastic response of the predator-prey system is investigated, and an analytical feedback control is designed to reshape the response of the ecosystem from the disturbed state back to the undisturbed one.Numerical simulations finally illustrate the accuracy and effectiveness of the proposed procedure.展开更多
In this paper, a nonautonomous predator-prey system based on a modified version of the Leslie-Gower scheme and Holling-type II scheme with delayed effect is investigated. The general criteria of integrable form on the...In this paper, a nonautonomous predator-prey system based on a modified version of the Leslie-Gower scheme and Holling-type II scheme with delayed effect is investigated. The general criteria of integrable form on the permanence are established. By constructing suitable Lyapunov functionals, a set of easily verifiable sufficient conditions are derived for global stability of any positive solutions to the展开更多
The purpose of this paper is to investigate positive steady states of a diffusive predator-prey system with predator cannibalism under homogeneous Neumann boundary conditions. With the help of implicit function theore...The purpose of this paper is to investigate positive steady states of a diffusive predator-prey system with predator cannibalism under homogeneous Neumann boundary conditions. With the help of implicit function theorem and energy integral method, nonexistence of non-constant positive steady states of the system is obtained, whereas coexistence of non-constant positive steady states is derived from topological degree theory. The results indicate that if dispersal rate of the predator or prey is sufficiently large, there is no nonconstant positive steady states. However, under some appropriate hypotheses, if the dispersal rate of the predator is larger than some positive constant, for certain ranges of dispersal rates of the prey, there exists at least one non-constant positive steady state.展开更多
In this paper, we mainly considered the dynamical behavior of a predator-prey system with Holling type II functional response and Allee-like effect on predator, including stability analysis of equilibria and Hopf bifu...In this paper, we mainly considered the dynamical behavior of a predator-prey system with Holling type II functional response and Allee-like effect on predator, including stability analysis of equilibria and Hopf bifurcation. Firstly, we gave some sufficient conditions to guarantee the existence, the local and global stability of equilibria as well as non-existence of limit cycles. By using the cobweb model, some cases about the existence of interior equilibrium are also illustrated with numerical outcomes. These existence and stability conclusions of interior equilibrium are also suitable in corresponding homogeneous reaction-diffusion system subject to the Neumann boundary conditions. Secondly, we theoretically deduced that our system has saddle-node bifurcation, transcritical bifurcation and Hopf bifurcation under certain conditions. Finally, for the Hopf bifurcation, we choose d as the bifurcation parameter and presented some numerical simulations to verify feasibility and effectiveness of the theoretical derivation corresponding to the existence of yk, respectively. The Hopf bifurcations are supercritical and limit cycles generated by the critical points are stable.展开更多
In this paper we analytically and numerically consider the dynamical behavior of a certain predator-prey system with Holling type II functional response, including local and global stability analysis, existence of lim...In this paper we analytically and numerically consider the dynamical behavior of a certain predator-prey system with Holling type II functional response, including local and global stability analysis, existence of limit cycles, transcritical and Hopf bifurcations. Mathematical theory derivation mainly focuses on the existence and stability of equilibrium point as well as threshold conditions for transcritical and Hopf bifurcation, which can in turn provide a theoretical support for numerical simulation. Numerical analysis indicates that theoretical derivation results are correct and feasible. In addition, it is successful to show that the dynamical behavior of this predator-prey system mainly depends on some critical parameters and mathematical relationships. All these results are expected to be meaningful in the study of the dynamic complexity of predatory ecosystem.展开更多
In this paper, a diffusive predator-prey system with general functional responses and prey-tactic sensitivities is studied. Providing such generality, we construct a Lyapunov function and we show that the positive con...In this paper, a diffusive predator-prey system with general functional responses and prey-tactic sensitivities is studied. Providing such generality, we construct a Lyapunov function and we show that the positive constant steady state is locally and globally asymptotically stable. With an eye on the biological interpretations, a numerical simulation is performed to illustrate the feasibility of the analytical findings.展开更多
This paper is concerned with optimal harvesting problems for a system consisting oftwo populations with age-structure and interaction of predator-prey. Existence and uniquenessof non-negative solutions to the system a...This paper is concerned with optimal harvesting problems for a system consisting oftwo populations with age-structure and interaction of predator-prey. Existence and uniquenessof non-negative solutions to the system and the continuous dependence of solutions on controlvariables are investigated. Existence of optimal policy is discussed, optimality conditions arederived by means of normal cone and adjoint system techniques.展开更多
In this paper, we considered a homogeneous reaction-diffusion predator-prey system with Holling type II functional response subject to Neumann boundary conditions. Some new sufficient conditions were analytically esta...In this paper, we considered a homogeneous reaction-diffusion predator-prey system with Holling type II functional response subject to Neumann boundary conditions. Some new sufficient conditions were analytically established to ensure that this system has globally asymptotically stable equilibria and Hopf bifurcation surrounding interior equilibrium. In the analysis of Hopf bifurcation, based on the phenomenon of Turing instability and well-done conditions, the system undergoes a Hopf bifurcation and an example incorporating with numerical simulations to support the existence of Hopf bifurcation is presented. We also derived a useful algorithm for determining direction of Hopf bifurcation and stability of bifurcating periodic solutions correspond to j ≠0 and j = 0, respectively. Finally, all these theoretical results are expected to be useful in the future study of dynamical complexity of ecological environment.展开更多
The predator-prey model for three species in which the right-hand sides are nonperiodic functions in time were considered, It's proved that the model is persistent under appropriate conditions.
基金Supported by the Social Science Foundation of Hebei Province(HB23TJO03)。
文摘A predator-prey model with prey dispersal and Holling type-Ⅱ functional response is investigated.In this model,the time delay due to the gestation of the predator and stagestructure for the predator are considered.By analyzing the corresponding characteristic equations,the local stability of each of the nonnegative equilibria is discussed.The existence of Hopf bifurcations at the positive equilibrium is established.By using Lyapunov functionals and LaSalle’s invariance principle,sufficient conditions are obtained for the global stability of the positive equilibrium,the nonnegative boundary equilibrium and the trivial equilibrium of the model,respectively.Numerical simulations are carried out to illustrate the main results.
基金Supported by the Social Science Foundation of Hebei Province(Grant No.HB23TJ003)the Science Research Project of Hebei Education Department(Grant No.BJK2024197)。
文摘This paper examines an epidemic predator-prey model with prey dispersal and Holling type-II functional response. In this model, it is assumed that the predator population suffers a transmissible disease. By analyzing the corresponding characteristic equations, the local stability of each of feasible equilibria and the existence of Hopf bifurcations at the coexistence equilibrium is addressed. Using Lyapunov functionals and LaSalle's invariance principle, we obtained the sufficient conditions for the global stability of the trivial equilibrium, the predator-extinction equilibrium, the disease-free equilibrium and the coexistence equilibrium, respectively. The paper also includes numerical simulations to illustrate the analytical results.
文摘This paper investigates the number of limit cycles in a predator-prey system with group defense,intially introduced by Wolkowicz and later examined by Rothe and Shafer in the 1980’s.Under the assumption of large prey growth,the system reduces to a perturbed singular system,whose limit cycles can be analyzed using geometric singular perturbation methods-primarily through the study of a slow-divergence integral.Our work completes partially the results previously obtained by Li and Zhu and by Hsu.We provide a comprehensive classification of all possible singular cycles capable of generating limit cycles and analyze the slow-divergence integral for the nine distinct types of cycle families that arise in a canard explosion.Based on these findings,we demonstrate that the maximum number of limit cycles emerging from the singular cycles is two in all cases,thereby confirming conjectures posed by Rothe-Shafer and Xiao-Ruan.
文摘One of the main objectives of artificial intelligence lies in the simulation of the behavior of living organisms;emotions are a fundamental part of life, and they cannot be left aside when simulating behavior. In this research, software is developed that simulates the behavior of birds with different characteristics. The latter interacts by considering different stimuli from the environment (external), and the internal state of the subject (objectives). To achieve this, a model of birds in the role of prey and predators is developed that focuses on the study of the interaction between these organisms that exhibit specific behaviors in their environment. This project is a seminal work that aims to represent the emotions of birds, and the latter caused by stimuli from a dynamic environment.
文摘Subject to the homogeneous Neumann boundary condition, a ratio-dependent predator-prey reaction diffusion model is discussed. An improved result for the model is derived, that is, the unique positive constant steady state is the global stability. This is done using the comparison principle and establishing iteration schemes involving positive solutions supremum and infimum. The result indicates that the two species will ultimately distribute homogeneously in space. In fact, the comparison argument and iteration technique to be used in this paper can be applied to some other models. This method deals with the not-existence of a non-constant positive steady state for some reaction diffusion systems, which is rather simple but sufficiently effective.
基金supported by the Sichuan Science and Technology Program of China(2018JY0480)the Natural Science Foundation Project of CQ CSTC of China(cstc2015jcyjBX0135)the National Nature Science Fundation of China(61503053)
文摘This article is focusing on a class of multi-delay predator-prey model with feedback controls and prey diffusion. By developing some new analysis methods and using the theory of differential inequalities as well as constructing a suitable Lyapunov function, we establish a set of easily verifiable sufficient conditions which guarantee the permanence of the system and the globally attractivity of positive solution for the predator-prey system.Furthermore, some conditions for the existence, uniqueness and stability of positive periodic solution for the corresponding periodic system are obtained by using the fixed point theory and some new analysis techniques. In additional, some numerical solutions of the equations describing the system are given to verify the obtained criteria are new, general, and easily verifiable. Finally, we still solve numerically the corresponding stochastic predator-prey models with multiplicative noise sources, and obtain some new interesting dynamical behaviors of the system.
文摘The nonlinear predator-prey reaction diffusion systems for singularly perturbed Robin Problems are considered. Under suitable conditions, the theory of differential inequalities can be used to study the asymptotic behavior of the solution for initial boundary value problems.
基金supported by the National Natural Science Foundation of China(11271120,11426099)the Project of Hunan Natural Science Foundation of China(13JJ3085)
文摘This paper deals with the global dynamical behaviors of the positive solutions for a parabolic type ratio-dependent predator-prey system with a crowding term in the prey equation, where it is assumed that the coefficient of the functional response is less than the coefficient of the intrinsic growth rates of the prey species. We demonstrated some special dynamical behaviors of the positive solutions of this system which the persistence of the coexistence of two species can be obtained when the crowding region in the prey equation only is designed suitably. Furthermore, we can obtain that under some conditions, the unique positive steady state solution of the system is globally asymptotically stable.
基金the National Natural Science Foundation of China(Nos.11772293 and12072312)Zhejiang Science and Technology Project(No.2019C03129)。
文摘An actual ecological predator-prey system often undergoes random environmental mutations owing to the impact of natural disasters and man-made destruction, which may destroy the balance between the species. In this paper,the stochastic dynamics of the nonlinear predator-prey system considering random environmental mutations is investigated, and a feedback control strategy is proposed to reshape the response of the predator-prey system against random abrupt environmental mutations. A delayed Markov jump system(MJS) is established to model such a predator-prey system. A novel first integral is constructed which leads to better approximation solutions of the ecosystem. Then, by applying the stochastic averaging method based on this novel first integral, the stochastic response of the predator-prey system is investigated, and an analytical feedback control is designed to reshape the response of the ecosystem from the disturbed state back to the undisturbed one.Numerical simulations finally illustrate the accuracy and effectiveness of the proposed procedure.
文摘In this paper, a nonautonomous predator-prey system based on a modified version of the Leslie-Gower scheme and Holling-type II scheme with delayed effect is investigated. The general criteria of integrable form on the permanence are established. By constructing suitable Lyapunov functionals, a set of easily verifiable sufficient conditions are derived for global stability of any positive solutions to the
基金partially supported by the National Natural Science Foundation of China(11371286)
文摘The purpose of this paper is to investigate positive steady states of a diffusive predator-prey system with predator cannibalism under homogeneous Neumann boundary conditions. With the help of implicit function theorem and energy integral method, nonexistence of non-constant positive steady states of the system is obtained, whereas coexistence of non-constant positive steady states is derived from topological degree theory. The results indicate that if dispersal rate of the predator or prey is sufficiently large, there is no nonconstant positive steady states. However, under some appropriate hypotheses, if the dispersal rate of the predator is larger than some positive constant, for certain ranges of dispersal rates of the prey, there exists at least one non-constant positive steady state.
文摘In this paper, we mainly considered the dynamical behavior of a predator-prey system with Holling type II functional response and Allee-like effect on predator, including stability analysis of equilibria and Hopf bifurcation. Firstly, we gave some sufficient conditions to guarantee the existence, the local and global stability of equilibria as well as non-existence of limit cycles. By using the cobweb model, some cases about the existence of interior equilibrium are also illustrated with numerical outcomes. These existence and stability conclusions of interior equilibrium are also suitable in corresponding homogeneous reaction-diffusion system subject to the Neumann boundary conditions. Secondly, we theoretically deduced that our system has saddle-node bifurcation, transcritical bifurcation and Hopf bifurcation under certain conditions. Finally, for the Hopf bifurcation, we choose d as the bifurcation parameter and presented some numerical simulations to verify feasibility and effectiveness of the theoretical derivation corresponding to the existence of yk, respectively. The Hopf bifurcations are supercritical and limit cycles generated by the critical points are stable.
文摘In this paper we analytically and numerically consider the dynamical behavior of a certain predator-prey system with Holling type II functional response, including local and global stability analysis, existence of limit cycles, transcritical and Hopf bifurcations. Mathematical theory derivation mainly focuses on the existence and stability of equilibrium point as well as threshold conditions for transcritical and Hopf bifurcation, which can in turn provide a theoretical support for numerical simulation. Numerical analysis indicates that theoretical derivation results are correct and feasible. In addition, it is successful to show that the dynamical behavior of this predator-prey system mainly depends on some critical parameters and mathematical relationships. All these results are expected to be meaningful in the study of the dynamic complexity of predatory ecosystem.
文摘In this paper, a diffusive predator-prey system with general functional responses and prey-tactic sensitivities is studied. Providing such generality, we construct a Lyapunov function and we show that the positive constant steady state is locally and globally asymptotically stable. With an eye on the biological interpretations, a numerical simulation is performed to illustrate the feasibility of the analytical findings.
基金Supported by the National Natural Science Foundation of China (10771048)the Research Project for Post-Graduates Creation of Zhejiang Province (YK2008054)
文摘This paper is concerned with optimal harvesting problems for a system consisting oftwo populations with age-structure and interaction of predator-prey. Existence and uniquenessof non-negative solutions to the system and the continuous dependence of solutions on controlvariables are investigated. Existence of optimal policy is discussed, optimality conditions arederived by means of normal cone and adjoint system techniques.
文摘In this paper, we considered a homogeneous reaction-diffusion predator-prey system with Holling type II functional response subject to Neumann boundary conditions. Some new sufficient conditions were analytically established to ensure that this system has globally asymptotically stable equilibria and Hopf bifurcation surrounding interior equilibrium. In the analysis of Hopf bifurcation, based on the phenomenon of Turing instability and well-done conditions, the system undergoes a Hopf bifurcation and an example incorporating with numerical simulations to support the existence of Hopf bifurcation is presented. We also derived a useful algorithm for determining direction of Hopf bifurcation and stability of bifurcating periodic solutions correspond to j ≠0 and j = 0, respectively. Finally, all these theoretical results are expected to be useful in the future study of dynamical complexity of ecological environment.
文摘The predator-prey model for three species in which the right-hand sides are nonperiodic functions in time were considered, It's proved that the model is persistent under appropriate conditions.
