一个具有阶段结构的捕食者食饵系统的周期解

本文研究一类捕食者具有阶段结构的捕食者食饵系统,利用重合度理论建立了这类系统正周期解的存在性结果.     

比率依赖型捕食者-食饵系统行波解的存在性

本文讨论一类比率依赖型捕食者 -食饵系统的反应扩散方程组 .首先 ,我们证明了时间周期定常解的存在性和稳定性 .其次 ,我们给出了扩散引起正常数平衡解失稳的条件 .最后 ,我们证明了比率依赖型捕食者 -食饵系统行波解的存在性和渐近性 .     

具有避难所的非自治两种群捕食者-食饵系统捕食者种群绝灭性研究

研究一类食饵具有避难所的非自治两种群捕食者-食饵系统,借助微分方程振荡性理论和微分方程比较原理得到了保证捕食者绝灭的一组充分性条件.     

具有收获和阶段结构的时滞脉冲的捕食-食饵模型

研究了食饵分布在不同斑块,捕食者具有阶段结构和收获的时滞脉冲的捕食-食饵模型.利用离散动力系统的频闪映射,得到了捕食者灭绝周期解的存在性和它的精确表达式.使用比较原理,得到了捕食者灭绝周期解全局渐近稳定的充分条件和系统的持久性.最后,用Matlab软件进行数值仿真验证了获得的结果.     

一类捕食者存在疾病的捕食系统传染病模型

建立并分析一类捕食者存在疾病的捕食系统传染病模型,模型中不考虑疾病对捕获率的影响.通过极限系统理论、Lyapunov稳定性理论分析和Bendixson判据,给出了各类平衡点存在及其全局稳定的条件,并得到了捕食者绝灭和疾病成为地方病的充分必要条件.     

一类非自治无时滞捕食食饵模型的持久性

主要针对一类非自治食饵具有阶段结构的捕食者非密度制约的捕食食饵模型进行了分析讨论,得到了种群灭绝以及持久的积分形式的充分条件,把捕食者密度制约的一些重要结论推广到捕食者非密度制约的情形,并且通过构造Lyapunov函数得到了系统的全局吸引性,最后利用数值模拟得到了当系统持久时周期模型的全局吸引性.     

带有非线性收获和妊娠时滞的微分代数捕食者-食饵系统的稳定性及Hopf分支

本文研究了一类同时带有非线性食饵收获和捕食者妊娠时滞的微分代数捕食者-食饵系统的稳定性及Hopf分支问题.利用了分支理论和稳定性理论,以捕食者妊娠时滞作为系统的分支参数,获得了所提出的新系统在正平衡点处系统稳定性的相关判据条件和Hopf分支的产生条件.推广了一般带有线性收获和时滞的微分代数捕食者-食饵系统的结论.     

带有非线性收获和妊娠时滞的微分代数捕食者-食饵系统的稳定性及Hopf分支（英文）

本文研究了一类同时带有非线性食饵收获和捕食者妊娠时滞的微分代数捕食者-食饵系统的稳定性及Hopf分支问题.利用了分支理论和稳定性理论,以捕食者妊娠时滞作为系统的分支参数,获得了所提出的新系统在正平衡点处系统稳定性的相关判据条件和Hopf分支的产生条件.推广了一般带有线性收获和时滞的微分代数捕食者-食饵系统的结论.     

一类滞后型非自治的捕食者-食饵系统的周期解

本文研究了一类滞后型三种群捕食者-食饵Lotka-Volterra系统.利用重合度理论 建立了这类系统正周期解的存在性判据.     

一类具有时滞的捕食者-猎物-共生者系统的研究

该文建立了具有时滞的捕食者-猎物-共生者系统模型,对模型的正性,持久性和局部稳定性记性了分析.得出此系统具有稳定的可能,正平衡点也具有渐近稳定的可能.最后用棉蚜生态系统中的瓢虫、棉蚜、蚂蚁的相关数据进行数值模拟,得出猎物和捕食者的发育历期(时滞)对整个系统具有重要影响,若发育历期过长,则整个系统将具有周期性的波动.     

Stationary distribution and extinction of a stochastic predator–prey model with distributed delay

In this paper, we focus on a stochastic predator–prey model with distributed delay. We first obtain the existence of a stationary distribution to the positive solutions by stochastic Lyapunov function method. Then we establish sufficient conditions for extinction of the predator population, that is, the prey population is survival and the predator population is extinct.     

A discrete prey–predator model preserving the dynamics of a structurally unstable Lotka–Volterra model

Leslie's method to construct a discrete two dimensional dynamical system dynamically consistent with the Lotka–Volterra type of competing two species ordinary differential equations is applied in a newly extended manner for the Lotka–Volterra prey–predator system which is structurally unstable. We show that, independently of the time step size, the derived discrete prey–predator system is dynamically consistent with the continuous counterpart, keeping the nature of neutrally stable periodic orbit. Further, we show that the extended method to construct the discrete prey–predator system can provide a dynamically consistent model also for the logistic Lotka–Volterra one.     

一类带时滞的阶段结构捕食模型的定性分析

研究了一类具有时滞和阶段结构的捕食模型系统,给出了系统持续生存的充分条件.利用比较定理和构造适当的Lyapunov泛函得到了该系统正平衡态全局渐近稳定的充分条件.     

三种群捕食-被捕食模型中具时滞的抛物系统

本文研究三种群食物链,其中第三种群是第二种群的捕食者,第二种群是第一种群的捕食者。我们用上下解方法研究具时滞的耦合半线性抛物方程组的动力学行为,给出了解的渐近性质。     

Interactions of Turing and Hopf bifurcations in an additional food provided diffusive predator-prey model

Complex spatiotemporal dynamics of a diffusive predator-prey system involving additional food supply to predator and intra-specific competition among predator, are investigated. We establish critical conditions of the occurrence of Turing instability, which are necessary and sufficient. Furthermore, we also establish conditions of the occurrence of codimension-2 Turing-Hopf bifurcation and Turing-Turing bifurcation, by exploring interactions of Turing bifurcations and Hopf bifurcation. For Turing-Hopf bifurcation, by analyzing normal form truncated to order 3 which are derived by applying normal form method, it is shown that under proper conditions, diffusive predator-prey system generates interesting spatial, temporal and spatiotemporal patterns, including a pair of spatially inhomogeneous steady states, a spatially homogeneous periodic solution and a pair of spatially inhomogeneous periodic solutions. And numerical simulations are also shown to support theory analysis. Moreover, it is found that proper intra-specific competition among predator helps generate complex spatiotemporal dynamics. And, proper additional food supply to predator helps control the population fluctuations of predator and prey, while large quantity and high quality of additional food supply will lead to the extinction of prey and make predator change the source of food, which finally destroy the ecosystem. These investigations might help understand complex spatiotemporal dynamics of predator-prey system involving additional food supply to predator and intra-specific competition among predator, and help conserve species in an ecosystem via supplying suitable additional food.     

Predator invasion in predator–prey model with prey-taxis in spatially heterogeneous environment

We consider a predator–prey model with prey-taxis and Holling-type II functional responses in a spatially heterogeneous environment to analyze the effects of prey-taxis and the heterogeneity of an environment on predator invasion. To achieve our goal, we investigate the stability of semi-trivial solution in which the predator is absent. It is known that both the predator diffusion and the death rate contribute to the predator invasion in a heterogeneous habitat when there is no prey-taxis. In this paper, we show that predator invasion is affected by the prey-taxis and diffusions of the prey-taxis model for a certain range of predator death rates in a heterogeneous environment. Furthermore, in cases where predator invasion by predator diffusion does not occur in a particular death rate range of the predator, predator invasion can occur by prey-taxis in a spatially heterogeneous habitat. In addition, we compare this phenomenon to the corresponding predator–prey model with ratio-dependent functional responses. It is observed that none of the predator’s diffusion and prey-taxis affect the predator’s invasion, and that only the predator’s death rate contributes to predator invasion for the model with ratio-dependent functional responses.     

A study of predator–prey models with the Beddington–DeAnglis functional response and impulsive effect

In this paper, the predator–prey system with the Beddington–DeAngelis functional response is developed, by introducing a proportional periodic impulsive catching or poisoning for the prey populations and a constant periodic releasing for the predator. The Beddington–DeAngelis functional response is similar to the Holling type II functional response but contains an extra term describing mutual interference by predators. This model has the potential to protect predator from extinction, but under some conditions may also lead to extinction of the prey. That is, the system exists a locally stable prey-eradication periodic solution when the impulsive period satisfies an inequality. The condition for permanence is established via the method of comparison involving multiple Liapunov̀ functions. Further, by numerical simulation method the influences of the impulsive perturbations and mutual interference by predators on the inherent oscillation are investigated. With the increasing of releasing for the predator, the system appears a series of complex phenomenon, which include (1) period-doubling, (2) chaos attractor, (3) period-halfing. (4) non-unique dynamics (meaning that several attractors coexist).     

POSITIVE STEADY STATES OF A DIFFUSIVE PREDATOR-PREY SYSTEM WITH PREDATOR CANNIBALISM

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.     

Positive solutions of certain nonlinear elliptic systems with self-diffusions: nondegenerate vs. degenerate diffusions

We discuss the existence of positive solutions to certain strongly-coupled nonlinear elliptic systems with self-diffusions under homogeneous Dirichlet boundary conditions. Using the global positive coexistence results for predator–prey, competition and symbiotic interactions between two species, sufficient conditions for the positive solutions of the degenerate self-diffusive systems are studied. We also investigate the local behavior, namely, the local existence, uniqueness and stability, of positive solutions for predator–prey and competition interactions. Our method is based on the decoupling technique and bifurcation theory.