一类具有阶段结构和时滞的捕食系统的持续生存和稳定性

我们提出和研究一类带有阶段结构和时滞的捕食模型,得到了种群持续生存的充分条件.研究了阶段结构和时滞对系统稳定性的影响,获得了系统发生Hopf分支和稳定性的条件以及轨道渐进稳定的周期解的存在性.     

A study on time-limited control of single-pest with stage-structure

Two kinds of time-limited pest control models of single-pest with stage-structure, which can be described by the boundary value problem of ordinary differential equation and impulsive differential equation, are presented according to the ways of artificial control (continuous control and impulsive control). The conditions under which the corresponding model has a solution are given. If the model has a solution, the corresponding aim of pest control can be achieved. The theoretical results show that both the mature and the immature pest should be controlled synchronously, otherwise the aims of pest control can not be achieved in a finite time. Finally, some discussions and numerical simulations show that the impulsive control is more practical than the continuous control.     

Dynamical behavior of a stochastic predator-prey model with stage structure for prey

Abstract

In the present paper, we focus on a stochastic predator-prey model with stage structure for prey. Firstly, by using the stochastic Lyapunov function method, we obtain sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of the positive solutions to the model. Then we establish sufficient conditions for extinction of the predator population in two cases. Some examples and numerical simulations are carried out to validate our analytical findings.     

对具阶段结构和生育脉冲的种群模型脉冲喷洒杀虫剂的动力学性质

研究了一个具有阶段结构,脉冲生育及在固定时刻对其喷洒杀虫剂的害虫种群模型的动力学性质.运用由频闪映射决定的离散动力系统,得到了具R icker功能函数系统的精确1-周期解,并讨论了它在临界条件下的稳定性.通过证明喷洒杀虫剂的时间对成年害虫有巨大的影响,得出结论喷洒杀虫剂的最好时间在季末,即在临近生育时期.     

Global Attractivity of Nonautonomous Inshore-Offshore Fishing Models with Stage-structure

The article deals with a nonautonomous fishing model with stage-structure in inshore and offshore. By using the theory of monotone of functional differential equation and the concave operator theory of functional differential equation, the stability of the positive periodic solution of a dynamical system representing the fishery are derived, and their globally attracting behaviour is discussed. A briefly biology meaning of the mathematical results is given.     

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.     

Hybrid approach for pest control with impulsive releasing of natural enemies and chemical pesticides: A plant–pest–natural enemy model

The agricultural pests can be controlled effectively by simultaneous use (i.e., hybrid approach) of biological and chemical control methods. Also, many insect natural enemies have two major life stages, immature and mature. According to this biological background, in this paper, we propose a three tropic level plant–pest–natural enemy food chain model with stage structure in natural enemy. Moreover, impulsive releasing of natural enemies and harvesting of pests are also considered. We obtain that the system has two types of periodic solutions: plant–pest-extinction and pest-extinction using stroboscopic maps. The local stability for both periodic solutions is studied using the Floquet theory of the impulsive equation and small amplitude perturbation techniques. The sufficient conditions for the global attractivity of a pest-extinction periodic solution are determined by the comparison technique of impulsive differential equations. We analyze that the global attractivity of a pest-extinction periodic solution and permanence of the system are evidenced by a threshold limit of an impulsive period depending on pulse releasing and harvesting amounts. Finally, numerical simulations are given in support of validation of the theoretical findings.     

单种群阶段结构的生育脉冲模型

本文研究单种群阶段结构生育脉冲的数学模型,通过研究其频闪映射所确定的离散动力系统,我们获得了生育脉冲的系统存在周期解及其稳定的阈值,阐述了阈值的生物意义.     

The Analysis of Model on Population Growth with Stage-structure in the Polluted Environment

In this paper,the authors considered a single-species model with stage-structure in a pollutedecological environment.Subject to the outside toxin input quantity being stable,the authors established thesufficient conditions under which the species will be permanent using Lyapunov method.At the same timebiological implications briefly of these results are discussed.     

Traveling wavefronts of a prey-predator diffusion system with stage-structure and harvesting

From a biological point of view, we consider a prey-predator-type free diffusion fishery model with stage-structure and harvesting. First, we study the stability of the nonnegative constant equilibria. In particular, the effect of harvesting on the stability of equilibria is discussed and supported with numerical simulation. Then, employing the upper and lower solution method, we show that when the wave speed is large enough there exists a traveling wavefront connecting the zero solution to the positive equilibrium of the system. Numerical simulation is also carried out to illustrate the main result.