一类比率型功能性反应捕食模型的稳定性分析

研究了一类具有比率型功能性反应的捕食模型,对模型进行了定性和稳定性分析,讨论了模型唯一正平衡点的存在条件,以及模型各个平衡点的性态.得到了各个平衡点全局渐近稳定的充分条件.通过绘制模型的相轨线,分析轨线的走向得到了原点全局渐近稳定的条件,并证明了模型不存在非平凡正周期解的条件,通过构造Lyapunov函数得到了模型的唯一正平衡点是全局渐近稳定的结论.     

一类含时滞的比率依赖捕食系统正平衡点的全局稳定性分析

讨论了一种食饵增长为Gilpin-Ayala型的比率依赖的食饵捕食者模型,利用第二加性复合矩阵原理证明线性化系统正轨道解的稳定性,结合系统在凸集中存在唯一的局部正平衡点,证明了正平衡点的全局渐近稳定性.结合数值模拟验证了所得结论的合理性,同时指出定理结论仅为充分条件,丰富完善了模型的动力学性质.     

Global Qualitative Analysis for a Ratio-Dependent Predator-Prey Model with Delay

A ratio-dependent predator-prey model with time lag for predator is proposed and analyzed. Mathematical analyses of the model equations with regard to boundedness of solutions, nature of equilibria, permanence, and stability are analyzed. We note that for a ratio-dependent system local asymptotic stability of the positive steady state does not even guarantee the so-called persistence of the system and, therefore, does not imply global asymptotic stability. It is found that an orbitally asymptotically stable periodic orbit exists in that model. Some sufficient conditions which guarantee the global stability of positive equilibrium are given.     

一类依比例依赖的捕食系统的性态分析

对一类依比例依赖的时滞捕食系统进行讨论.首先,对系统中解的最终有界性、平衡点的存在性及稳定性进行了分析.进一步,利用微分比较定理讨论了系统的永久持续生存和灭绝,得到了系统的永久持续生存和灭绝的条件.     

一类基于比率的捕食-食饵系统的全局稳定性分析

研究一类基于比率和具第Ⅲ类功能性反应的捕食-食饵系统．通过分析正平衡点的局部稳定性给出了系统正平衡点全局渐近稳定以及系统存在极限环的条件．运用Hopf分支理论讨论了当正平衡点是非双曲型时的情形．     

食饵具庇护所的基于比率捕食-食饵模型的全局稳定性和分支

研究一类食饵具庇护所的基于比率捕食-食饵模型,得到该模型的全局稳定、极限环以及Hopf分支等的一系列充分条件.研究表明当模型捕食种群转化率、死亡率和半饱和常数满足一定条件时,食饵庇护量不影响捕食、食饵两种群的共存.一旦该条件不满足,则食饵庇护量具有稳定化作用.数值模拟验证了所得结论的可行性.     

具有比率依赖随机食物链系统的定性分析

研究了一类具有比率依赖随机食物链系统的动力学行为,运用随机微分方程比较定理和伊藤公式,证明了系统存在唯一正解,给出随机食物链系统的持久性和物种趋于灭绝的条件.最后,通过数值模拟验证所得结果的正确性.     

一类具有时滞和基于比率的捕食扩散系统

研究了一类具有时滞和基于比率的非自治捕食-食饵扩散模型,通过利用微分不等式、比较原理和构造适当的Lyapunov泛函,得到了该系统持续生存和存在全局稳定的正周期解的充分条件.     

Periodic Solution for a Stochastic Non-autonomous Predator-Prey Model with Holling II Functional Response

A biological population may be subjected to stochastic disturbance and exhibit periodicity. In this paper, a stochastic non-autonomous predator-prey system with Holling II functional response is proposed, and the existence of a unique positive solution is derived. We give sufficient conditions for extinction and strong persistence in the mean by analyzing a corresponding one-dimensional stochastic system. Also we establish the existence of positive periodic solutions for this stochastic non-autonomous predator-prey system. Finally, we use numerical simulations to illustrate our results and we present some conclusions and future directions. The results of this paper provide methods for other stochastic population models, which we hope to analyze in the future.

     

一类具有时滞和基于比率的三种群捕食-食饵系统的周期解的存在性

研究一类具有时滞和基于比率的三种群捕食-食铒二斑块系统，利用重合度理论的连续定理建立了这类系统的周期解的存在性判据．     

具有时滞和可变营养消耗率的比率型Chemostat模型稳定性分析

考虑了一类具有时滞和可变营养消耗率、增长函数为比率确定型的微生物连续培养模型.首先,详细地讨论了解的存在性、有界性、平衡点的局部渐近稳定性以及Hopf分支.其次,利用Lyapunov-LaSalle不变性原理证明了边界平衡点的全局渐近性.最后,利用时滞微分系统解的极限集的一些性质,证明了当正平衡点存在时,对任意时滞系统是一致持久的.     

一类具有反馈控制和Holling-Ⅲ类功能性反应的比率依赖离散时滞模型的持久性

主要讨论一类基于比率的具有反馈控制变量的Holling-Ⅲ离散模型,通过运用差分不等式的有关结论和一些计算技巧,得到了保证该系统持久性的充分性条件,数值模拟也证明结论是可行的.     

具有连续时滞和基于比率的非自治捕食扩散系统的持续生存

研究具有连续时滞和基于比率的非自治捕食扩散系统.证明了该系统一致持久性及任何正解全局渐近稳定性的充分条件.     

Adaptive Evolution Analysis of a Predator-Prey Model With Group Defense北大核心CSCD

Based on the theoretical framework of adaptive dynamics, the evolution of the predator-prey model with functional response of group defense effect on the predator handling time, was investigated. Firstly, in view of the interaction of predator populations with interspecific competition, the evolutionary conditions for a single predator population to split into 2 populations with different strategies through evolutionary branching were given. Secondly, when the ecological equilibrium of the model is unstable and the system has a limit cycle, the population will have strong coexistence under large mutation, but this coexistence will be evolutionarily unstable. Finally, the conclusions for the model with Holling-Ⅱ type functional response were compared. The results indicate that, with a sufficiently large prey carrying capacity, group defense effects can evolutionarily lead to the extinction of predators. © 2023 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

具有食饵避难的Leslie-Gower捕食系统最优收获分析

研究了一类具有食饵避难的Leslie-Gower捕食与被捕食系统收获模型,利用Hurwitz判据,得到了正平衡点局部渐近稳定,进一步构造了适当的Lyapunov函数,证明了正平衡点的全局渐近稳定性.并且在捕获努力量假说下,对发生食饵避难的两种群同时捕获,考虑了生态经济平衡点的存在性和利用Pontryagin最大值原理对两种群进行最优收获,得到当贴现率为零时,既保持了生态平衡,又使得在渔业开发过程中取得最大经济利益.     

On the Dynamics of an Impulsive Reaction-Diffusion Predator-Prey System with Ratio-Dependent Functional Response

An impulsive reaction-diffusion periodic predator-prey system with ratio-dependent functional response is investigated in the present paper. Sufficient conditions for the ultimate boundedness and permanence of the predator-prey system are established based on the upper and lower solution method and comparison theory of differential equation. By constructing appropriate auxiliary function, the conditions for the existence of a unique globally stable positive periodic solution are also obtained. Some numerical examples are presented to verify our results. A discussion is given in the end of the paper.     

具有食饵避难的Leslie-Gower最优税收模型分析

建立了发生食饵避难的Leslie-Gower捕食与被捕食系统模型,考虑对捕食种群进行有选择捕获.通过控制税收量加以管理来保护渔业资源不被过渡开发,且讨论了系统平衡点的存在性和稳定性,运用Pontryagin最大值原理得到了达到最优税收量的最优平衡解.     

捕食者和食饵均带有扩散的随机捕食-食饵模型动力学分析

考虑了斑块环境下捕食者种群和食饵种群分别在n个斑块扩散的随机捕食 食饵模型.利用Lyapunov函数法证明了对任意给定的初始值,随机系统全局正解的存在唯一性,并对其进行了有界性分析.此外给出了食饵种群及整个系统灭绝的充分条件.最后通过数值模拟验证了所得理论的正确性.     

A General Predator-Prey Model

We consider n = 2 populations of animals or plants that are living in mutual predator-prey relations or are pairwise neutral to each other. We assume the temporal development of the population densities to be described by a system of differential equations which has an equilibrium state solution. We at first give sufficient conditions for this equilibrium state to be asymptotically stable by linearizing the system around it. Then we derive sufficient conditions for asymptotic stability by Lyapunov’s method. Finally we investigate a discretization of the Volterra-Lotka model.