连续收获捕食者与脉冲存放食饵的阶段结构捕食-食饵模型的全局吸引和一致持久

研究了一个捕食者具连续收获与食饵具脉冲存放的阶段结构时滞捕食-食饵模型．根据生物资源管理的实际,改进了捕食者具阶段结构的捕食-食饵模型,即原来假设每个捕食者个体都具有相同的捕食食饵的能力．假设捕食者按年龄分为两个阶段,即幼体和成体,而且幼体无能力捕食食饵．得到了捕食者灭绝周期解全局吸引和系统持久的充分条件．结论说明了脉冲存放食饵对系统的持久起了重要的作用,并且为生物资源管理提供了策略基础．数值分析也进一步说明了系统的动力学性质．     

Permanence in a periodic delay logistic system subject to constant impulsive stocking

In this paper, a periodic impulsive delay single population system with hereditary effect is established. The constant impulse is realized at fixed moments of time. By using the comparison principle of impulsive differential equations and analysis techniques, the permanence of the system is obtained. It shows that the constant impulsive stocking plays an important role. Numerical simulations are presented to substantiate our analytical results. Copyright © 2009 John Wiley & Sons, Ltd.     

Permanence and stability of an Ivlev-type predator–prey system with impulsive control strategies

In this paper, we study a predator–prey system with an Ivlev-type functional response and impulsive control strategies containing a biological control (periodic impulsive immigration of the predator) and a chemical control (periodic pesticide spraying) with the same period, but not simultaneously. We find conditions for the local stability of the prey-free periodic solution by applying the Floquet theory of an impulsive differential equation and small amplitude perturbation techniques to the system. In addition, it is shown that the system is permanent under some conditions by using comparison results of impulsive differential inequalities. Moreover, we add a forcing term into the prey population’s intrinsic growth rate and find the conditions for the stability and for the permanence of this system.     

An impulsive controlled eco-epidemic model with disease in the prey

In this paper, we investigate the dynamic behavior of an eco-epidemic model with impulsive control strategy. By using Floquet theorem of impulsive differential equation, we show there is a globally stable prey eradication periodic solution when the impulsive period is less than some critical value. We study the permanence of the system. Numerical simulations show that the complex dynamics of the system depends on the values of impulsive period and impulsive perturbation, for example double period, triple period solutions.     

An impulsive predator–prey system with modified Leslie–Gower and Holling type II schemes

An impulsive predator–prey system with modified Leslie–Gower and Holling-type II schemes is presented. By using the Floquet theory of impulsive equation and small amplitude perturbation method, the globally asymptotical stability of prey-free positive periodic solution and the permanence of system are discussed. The corresponding threshold conditions are obtained respectively. Finally, numerical simulations are given.     

A predator–prey system with two impulses on the diseased prey and a Beddington–DeAngelis response

A predator–prey system with two impulses on the diseased prey is formulated and analyzed for the purpose of integrated pest management. The local and global stability of the susceptible pest‐eradication periodic solution, as well as the permanence of the system, are obtained under the sufficient conditions by means of Floquet's theory for impulsive differential equations. Finally, we interpret our mathematical results. Copyright © 2009 John Wiley & Sons, Ltd.     

食饵具脉冲扰动与捕食者具连续收获的时滞捕食-食饵模型

本文讨论了与生物资源管理相关的食饵具脉冲扰动与捕食者具连续收获的时滞捕食-食饵模型,得到了捕食者灭绝周期解的全局吸引和系统持久的充分条件.也证明了系统的所有解的一致完全有界.我们的结论为现实的生物资源管理提供了可靠的策略依据,也丰富了脉冲时滞微分方程的理论.     

Analysis of a stage structured predator–prey Gompertz model with disturbing pulse and delay

In this paper, we introduce a general and robust prey-dependent consumption predator–prey Gompertz model with periodic harvesting for the prey and stage structure for the predator with constant maturation time delay and perform a systematic mathematical and ecological study. Sufficient conditions which guarantee the global attractivity of predator-extinction periodic solution and permanence of the system are obtained. We also prove that constant maturation time delay and impulsive catching or poisoning for the prey can bring great effects on the dynamics of system by numerical analysis. Our results provide reliable tactic basis for the practical pest management.     

Survival analysis for a periodic predator–prey model with prey impulsively unilateral diffusion in two patches

In this paper, we study a periodic predator–prey system with prey impulsively unilateral diffusion in two patches. Firstly, based on the results in [41], sufficient conditions on the existence, uniqueness and globally attractiveness of periodic solution for predator-free and prey-free systems are presented. Secondly, by using comparison theorem of impulsive differential equation and other analysis methods, sufficient and necessary conditions on the permanence and extinction of prey species x with predator have other food source are established. Finally, the theoretical results both for non-autonomous system and corresponding autonomous system are confirmed by numerical simulations, from which we can see some interesting phenomena happen.     

脉冲效应下一个捕食-食饵系统的灭绝与持续生存

在这篇文章中 ,我们拓展了传统的Lokta volterra模型 ,考虑了一个具脉冲效应的捕食 食饵系统 ,利用脉冲比较原理及Lyapunov函数证明了该系统的灭绝性与持续生存     

An impulsive periodic predator–prey system with Holling type III functional response and diffusion

This paper studies an impulsive two species periodic predator–prey Lotka–Volterra type dispersal system with Holling type III functional response in a patchy environment, in which the prey species can disperse among n different patches, but the predator species is confined to one patch and cannot disperse. Conditions for the permanence and extinction of the predator–prey system, and for the existence of a unique globally stable periodic solution are established. Numerical examples are shown to verify the validity of our results.     

Dynamics of impulsive reaction–diffusion predator–prey system with Holling type III functional response

An impulsive reaction–diffusion periodic predator–prey system with Holling type III 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 an 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 at the end.     

一类具有脉冲收获和投放的捕食系统的研究

建立了一类具有Ivlev功能反应函数的捕食系统,引入二次脉冲对该系统中捕食者进行作用,讨论了系统的有界性,利用Floquet理论和小振幅扰动方法,得出了食饵灭绝的周期解的局部稳定性和该系统最终持久生存的条件.     

The dynamical behavior of a predator–prey system with Gompertz growth function and impulsive dispersal of prey between two patches

In this paper, we investigate a predator–prey model with Gompertz growth function and impulsive dispersal of prey between two patches. Using the dynamical properties of single‐species model with impulsive dispersal in two patches and comparison principle of impulsive differential equations, necessary and sufficient criteria on global attractivity of predator‐extinction periodic solution and permanence are established. Finally, a numerical example is given to illustrate the theoretical results. Copyright © 2015 John Wiley & Sons, Ltd.     

捕食者具脉冲扰动与食饵具有化学控制的阶段结构时滞捕食-食饵模型

讨论了与害虫治理相关的一类捕食者具脉冲扰动与食饵具有化学控制的阶段结构时滞捕食-食饵模型,得到了害虫灭绝周期解的全局吸引和系统持久的充分条件,也证明了系统的所有解的一致完全有界．得出的结论为现实的害虫治理提供了可靠的策略依据．     

The effects of impulsive harvest on a predator–prey system with distributed time delay

A kind of predator–prey system with distributed time delay and impulsive harvest is firstly presented and then the effects of impulsive harvest on the system are discussed by means of chain transform. By using the Floquet’s theory and the comparison theorem of impulsive differential equation, the thresholds between permanence and extinction of each species are obtained as functions of model parameters. It is proved that the impulsive period and the proportion of the impulsive harvest will ultimately affect the fate of each species. Finally, the theoretical results obtained in this paper are confirmed by numerical simulations.     

The dynamics of an impulsive delay predator–prey model with stage structure and Beddington-type functional response

In this paper, an impulsive delay predator–prey model with stage structure and Beddington-type functional response is established. By using the discrete dynamical system determined by the stroboscopic map, we obtain the existence and global attractivity of the predator-extinction periodic solution. By use of the theory on delay and impulsive differential equation, we study the permanence of the system. Finally, an example is given to show the effectiveness of the main results.     

收获捕食者的时滞脉冲捕食模型

讨论了与可再生生物资源管理相关的食饵具脉冲扰动与捕食者具连续收获的阶段结构时滞捕食-食饵模型,得到了捕食者灭绝周期解的全局吸引和系统持久的充分条件.也证明了系统的所有解的一致完全有界.结论为现实的可再生生物资源管理提供了可靠的策略依据.     

The dynamical behaviors of a Ivlev-type two-prey two-predator system with impulsive effect

In this paper, considering the strategy of integrated Pest Management (IPM), a class of two-prey two-predator system with the Ivlev-type functional response and impulsive effect at different fixed time is established. By using impulsive comparison theorem, Floquent theory and small amplitude perturbation skill, the sufficient conditions for the system to be extinct of prey and permanence are proved. Moreover, we give two sufficient conditions for the extinction of one of two prey and remaining three species are permanent. Numerical simulation shows that there exist complex dynamics for system, such as symmetry-breaking pitchfork bifurcation, periodic doubling bifurcation, chaos, periodic halving cascade. Lastly, a brief discussion is given.     

Impulsive perturbations in a predator–prey model with dormancy of predators

In this paper, a predator–prey model consisting of active and dormant states of predators with impulsive control strategy is established. Using Floquet theories, the small amplitude perturbation technique and the piecewise Lyapunov function method, the conditions of local and global asymptotical orbital stability of the prey-eradication periodic solution are obtained. The boundness and permanence of the impulsive system are proved by the comparison principle. Through numerical simulations, the effects of the impulsive perturbation on the inherent oscillation are investigated, which implies that the impulsive perturbation can lead to period-doubling bifurcation, chaos, and period-halving bifurcation. Moreover, the effects of the impulsive perturbation and hatching rate on the chaos of the system are comparatively studied by numerical simulation. These obtained results can be useful for ecosystem management and for explaining complex phenomena of ecosystems.