This paper deals with a Lotka-Volterra predator-prey model with a crowding term in the predator equation.We obtain a critical value λ1^D(Ω0),and demonstrate that the existence of the predator inΩ0 only depends on t...This paper deals with a Lotka-Volterra predator-prey model with a crowding term in the predator equation.We obtain a critical value λ1^D(Ω0),and demonstrate that the existence of the predator inΩ0 only depends on the relationship of the growth rateμof the predator and λ1^D(Ω0),not on the prey.Furthermore,whenμ<λ1^D(Ω0),we obtain the existence and uniqueness of its positive steady state solution,while whenμ≥λ1^D(Ω0),the predator and the prey cannot coexist inΩ0.Our results show that the coexistence of the prey and the predator is sensitive to the size of the crowding regionΩ0,which is different from that of the classical Lotka-Volterra predator-prey model.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 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.
In this paper, we consider Lotka-Volterra predator-prey model between one and three species. Two cases are distinguished. The first is Lotka-Volterra model of one prey-three predators and the second is Lotka-Volterra ...In this paper, we consider Lotka-Volterra predator-prey model between one and three species. Two cases are distinguished. The first is Lotka-Volterra model of one prey-three predators and the second is Lotka-Volterra model of one predator-three preys. The existence conditions of nonnega-tive equilibrium points are established. The local stability analysis of the system is carried out.展开更多
The main purpose of this article is considering the persistence non-autonomous Lotka-Volterra system with predator-prey ratio-dependence and density dependence. We get the sufficient conditions of persistence of syste...The main purpose of this article is considering the persistence non-autonomous Lotka-Volterra system with predator-prey ratio-dependence and density dependence. We get the sufficient conditions of persistence of system, further have the necessary conditions, also the uniform persistence condition, which can be easily checked for the model is obtained.展开更多
The Lotka-Volterra predator-prey model is widely used in many disciplines such as ecology and economics. The model consists of a pair of first-order nonlinear differential equations. In this paper, we first analyze th...The Lotka-Volterra predator-prey model is widely used in many disciplines such as ecology and economics. The model consists of a pair of first-order nonlinear differential equations. In this paper, we first analyze the dynamics, equilibria and steady state oscillation contours of the differential equations and study in particular a well-known problem of a high risk that the prey and/or predator may end up with extinction. We then introduce exogenous control to reduce the risk of extinction. We propose two control schemes. The first scheme, referred as convergence guaranteed scheme, achieves very fine granular control of the prey and predator populations, in terms of the final state and convergence dynamics, at the cost of sophisticated implementation. The second scheme, referred as on-off scheme, is very easy to implement and drive the populations to steady state oscillation that is far from the risk of extinction. Finally we investigate the robustness of these two schemes against parameter mismatch and observe that the on-off scheme is much more robust. Hence, we conclude that while the convergence guaranteed scheme achieves theoretically optimal performance, the on-off scheme is more attractive for practical applications.展开更多
In this paper,we mainly study the propagation properties of a nonlocal dispersal predator-prey system in a shifting environment.It is known that Choi et al.[J Differ Equ,2021,302:807-853]studied the persistence or ext...In this paper,we mainly study the propagation properties of a nonlocal dispersal predator-prey system in a shifting environment.It is known that Choi et al.[J Differ Equ,2021,302:807-853]studied the persistence or extinction of the prey and of the predator separately in various moving frames.In particular,they achieved a complete picture in the local diffusion case.However,the question of the persistence of the prey and of the predator in some intermediate moving frames in the nonlocal diffusion case was left open in Choi et al.'s paper.By using some a prior estimates,the Arzelà-Ascoli theorem and a diagonal extraction process,we can extend and improve the main results of Choi et al.to achieve a complete picture in the nonlocal diffusion case.展开更多
In this paper we study a bilinear optimal control problem for a diffusive Lotka-Volterra competition model with chemo-repulsion in a bounded domain of ℝ^(ℕ),N=2,3.This model describes the competition of two species in...In this paper we study a bilinear optimal control problem for a diffusive Lotka-Volterra competition model with chemo-repulsion in a bounded domain of ℝ^(ℕ),N=2,3.This model describes the competition of two species in which one of them avoid encounters with rivals through a chemo-repulsion mechanism.We prove the existence and uniqueness of weak-strong solutions,and then we analyze the existence of a global optimal solution for a related bilinear optimal control problem,where the control is acting on the chemical signal.Posteriorly,we derive first-order optimality conditions for local optimal solutions using the Lagrange multipliers theory.Finally,we propose a discrete approximation scheme of the optimality system based on the gradient method,which is validated with some computational experiments.展开更多
为了描述移动环境轻度恶化对两个弱合作物种的持久性产生的影响,本文考虑一类带有与时空均相关的恒正内禀增长函数的格上Lotka-Volterra合作系统。通过构造合适的上下解并结合单调迭代的方法证明了系统存在两组受迫行波解。In order to ...为了描述移动环境轻度恶化对两个弱合作物种的持久性产生的影响,本文考虑一类带有与时空均相关的恒正内禀增长函数的格上Lotka-Volterra合作系统。通过构造合适的上下解并结合单调迭代的方法证明了系统存在两组受迫行波解。In order to characterize the effect of mild deterioration of the shifting environment on the two weakly cooperative species persistence, we consider a class of the lattice Lotka-Volterra cooperative systems with a constant positive intrinsic growth function that is spatio-temporally correlated. By constructing suitable upper and slower solutions combined with the method of monotone iteration, we prove that there exist two sets of forced traveling wave solutions for the system.展开更多
本文研究了移动环境下一类具有时滞的Lotka-Volterra合作系统行波解的存在性。利用单调迭代方法,通过构造合适的上下解,证明了当环境运动速度c>max{ c1∗,c2∗}时,系统连接两边界平衡点的行波解的存在性。Existence of traveling wave ...本文研究了移动环境下一类具有时滞的Lotka-Volterra合作系统行波解的存在性。利用单调迭代方法,通过构造合适的上下解,证明了当环境运动速度c>max{ c1∗,c2∗}时,系统连接两边界平衡点的行波解的存在性。Existence of traveling wave front solutions is established for diffusive and cooperative Lotka-Volterra system with delays in a shifting environment. Using the method of monotone iteration and by constructing appropriate upper and lower solutions, it is proven that when the environmental movement speed is c>max{ c1∗,c2∗}, there exist traveling wave solutions that connect the boundary equilibrium points of the system.展开更多
考虑在移动环境下局部扩散三种群Lotka-Volterra竞争合作系统行波解的存在性,并假设此系统的内禀增长率函数恒大于某正常数。通过构造一对有序的上下解并利用单调迭代技巧和波动引理,证明了系统的非负受迫行波的存在性。We consider the...考虑在移动环境下局部扩散三种群Lotka-Volterra竞争合作系统行波解的存在性,并假设此系统的内禀增长率函数恒大于某正常数。通过构造一对有序的上下解并利用单调迭代技巧和波动引理,证明了系统的非负受迫行波的存在性。We consider the existence of traveling wave solutions for Lotka-Volterra competitive-cooperative system with three-species under a shifting habitat, and assume that the intrinsic growth rate functions of this system are greater than the normal numbers. We prove the existence of non-negative forced traveling waves of the system by constructing a pair of upper and lower solutions and using monotonic iterative techniques and the fluctuation lemma.展开更多
In this paper, the dynamic properties of a discrete predator-prey model are discussed. The properties of non-hyperbolic fixed points and hyperbolic fixed points of the model are analyzed. First, by using the classic S...In this paper, the dynamic properties of a discrete predator-prey model are discussed. The properties of non-hyperbolic fixed points and hyperbolic fixed points of the model are analyzed. First, by using the classic Shengjin formula, we find the existence conditions for fixed points of the model. Then, by using the qualitative theory of ordinary differential equations and matrix theory we indicate which points are hyperbolic and which are non-hyperbolic and the associated conditions.展开更多
基金the Hunan Provincial Natural Science Foundation of China(2019JJ40079,2019JJ50160)the Scientific Research Fund of Hunan Provincial Education Department(16A071,19A179)the National Natural Science Foundation of China(11701169)。
文摘This paper deals with a Lotka-Volterra predator-prey model with a crowding term in the predator equation.We obtain a critical value λ1^D(Ω0),and demonstrate that the existence of the predator inΩ0 only depends on the relationship of the growth rateμof the predator and λ1^D(Ω0),not on the prey.Furthermore,whenμ<λ1^D(Ω0),we obtain the existence and uniqueness of its positive steady state solution,while whenμ≥λ1^D(Ω0),the predator and the prey cannot coexist inΩ0.Our results show that the coexistence of the prey and the predator is sensitive to the size of the crowding regionΩ0,which is different from that of the classical Lotka-Volterra predator-prey model.
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 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.
文摘In this paper, we consider Lotka-Volterra predator-prey model between one and three species. Two cases are distinguished. The first is Lotka-Volterra model of one prey-three predators and the second is Lotka-Volterra model of one predator-three preys. The existence conditions of nonnega-tive equilibrium points are established. The local stability analysis of the system is carried out.
文摘The main purpose of this article is considering the persistence non-autonomous Lotka-Volterra system with predator-prey ratio-dependence and density dependence. We get the sufficient conditions of persistence of system, further have the necessary conditions, also the uniform persistence condition, which can be easily checked for the model is obtained.
文摘The Lotka-Volterra predator-prey model is widely used in many disciplines such as ecology and economics. The model consists of a pair of first-order nonlinear differential equations. In this paper, we first analyze the dynamics, equilibria and steady state oscillation contours of the differential equations and study in particular a well-known problem of a high risk that the prey and/or predator may end up with extinction. We then introduce exogenous control to reduce the risk of extinction. We propose two control schemes. The first scheme, referred as convergence guaranteed scheme, achieves very fine granular control of the prey and predator populations, in terms of the final state and convergence dynamics, at the cost of sophisticated implementation. The second scheme, referred as on-off scheme, is very easy to implement and drive the populations to steady state oscillation that is far from the risk of extinction. Finally we investigate the robustness of these two schemes against parameter mismatch and observe that the on-off scheme is much more robust. Hence, we conclude that while the convergence guaranteed scheme achieves theoretically optimal performance, the on-off scheme is more attractive for practical applications.
基金supported by the National Natural Science Foundation of China(12171039,12271044)。
文摘In this paper,we mainly study the propagation properties of a nonlocal dispersal predator-prey system in a shifting environment.It is known that Choi et al.[J Differ Equ,2021,302:807-853]studied the persistence or extinction of the prey and of the predator separately in various moving frames.In particular,they achieved a complete picture in the local diffusion case.However,the question of the persistence of the prey and of the predator in some intermediate moving frames in the nonlocal diffusion case was left open in Choi et al.'s paper.By using some a prior estimates,the Arzelà-Ascoli theorem and a diagonal extraction process,we can extend and improve the main results of Choi et al.to achieve a complete picture in the nonlocal diffusion case.
基金supported by Vicerrectoría de Investigación y Extensión of Universidad Industrial de Santander,Colombia,project 3704.
文摘In this paper we study a bilinear optimal control problem for a diffusive Lotka-Volterra competition model with chemo-repulsion in a bounded domain of ℝ^(ℕ),N=2,3.This model describes the competition of two species in which one of them avoid encounters with rivals through a chemo-repulsion mechanism.We prove the existence and uniqueness of weak-strong solutions,and then we analyze the existence of a global optimal solution for a related bilinear optimal control problem,where the control is acting on the chemical signal.Posteriorly,we derive first-order optimality conditions for local optimal solutions using the Lagrange multipliers theory.Finally,we propose a discrete approximation scheme of the optimality system based on the gradient method,which is validated with some computational experiments.
文摘为了描述移动环境轻度恶化对两个弱合作物种的持久性产生的影响,本文考虑一类带有与时空均相关的恒正内禀增长函数的格上Lotka-Volterra合作系统。通过构造合适的上下解并结合单调迭代的方法证明了系统存在两组受迫行波解。In order to characterize the effect of mild deterioration of the shifting environment on the two weakly cooperative species persistence, we consider a class of the lattice Lotka-Volterra cooperative systems with a constant positive intrinsic growth function that is spatio-temporally correlated. By constructing suitable upper and slower solutions combined with the method of monotone iteration, we prove that there exist two sets of forced traveling wave solutions for the system.
文摘本文研究了移动环境下一类具有时滞的Lotka-Volterra合作系统行波解的存在性。利用单调迭代方法,通过构造合适的上下解,证明了当环境运动速度c>max{ c1∗,c2∗}时,系统连接两边界平衡点的行波解的存在性。Existence of traveling wave front solutions is established for diffusive and cooperative Lotka-Volterra system with delays in a shifting environment. Using the method of monotone iteration and by constructing appropriate upper and lower solutions, it is proven that when the environmental movement speed is c>max{ c1∗,c2∗}, there exist traveling wave solutions that connect the boundary equilibrium points of the system.
文摘考虑在移动环境下局部扩散三种群Lotka-Volterra竞争合作系统行波解的存在性,并假设此系统的内禀增长率函数恒大于某正常数。通过构造一对有序的上下解并利用单调迭代技巧和波动引理,证明了系统的非负受迫行波的存在性。We consider the existence of traveling wave solutions for Lotka-Volterra competitive-cooperative system with three-species under a shifting habitat, and assume that the intrinsic growth rate functions of this system are greater than the normal numbers. We prove the existence of non-negative forced traveling waves of the system by constructing a pair of upper and lower solutions and using monotonic iterative techniques and the fluctuation lemma.
文摘In this paper, the dynamic properties of a discrete predator-prey model are discussed. The properties of non-hyperbolic fixed points and hyperbolic fixed points of the model are analyzed. First, by using the classic Shengjin formula, we find the existence conditions for fixed points of the model. Then, by using the qualitative theory of ordinary differential equations and matrix theory we indicate which points are hyperbolic and which are non-hyperbolic and the associated conditions.
