EXISTENCE AND GLOBAL ATTRACTIVITY OF POSITIVE SOLUTIONS OF A NONAUTONOMOUS LOGISTIC TYPE MODEL WITH QUADRATIC NONLINEARITY

Consider the nonautonomous logistic modelwhere {pn} is a sequence of positive real numbers, {kn} is a sequence of non-negative integers satisfying We obtainnew sufficient conditions for the attractivity of the equilibrium x = x of the model. Our results improve ones which were established by Gapalsamy and Ladas recently, and solve some research projects posed by Kocic and Ladas in [7].     

非自治阶段结构捕食系统的持续生存

研究了非自治阶段结构捕食幼年系统解的持久性，得到了该系统持续生存和全局吸引的条件。     

Global attractivity of an almost periodic N-species nonlinear ecological competitive model

By using comparison theorem and constructing suitable Lyapunov functional, we study the following almost periodic nonlinear N-species competitive Lotka-Volterra model:

     

一类脉冲扩散与时滞的捕食-食饵模型研究

运用脉冲时滞微分方程的比较理论,频闪映射和一些分析方法,讨论了一类捕食者具有脉冲扩散、食饵具有阶段结构的捕食-食饵模型得到了成熟食饵灭绝周期解的全局吸引和系统持久的充分条件,证明了系统的所有解是一致完全有界的.最后通过举例并进行数值模拟说明所得结果的正确性.     

Global dynamics and bifurcation of a perturbed Sigmoid Beverton–Holt difference equation

T. Wanner We investigate global dynamics of the equation where the parameters b,c, and f are nonnegative numbers with condition b + c > 0,f ≠ 0 and the initial conditions x_?1,x₀ are arbitrary nonnegative numbers such that x_?1+x₀>0. We obtain precise characterization of basins of attraction of all attractors of this equation and describe the dynamics in terms of bifurcations of period‐two solutions. Copyright © 2015 John Wiley & Sons, Ltd.     

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.     

Existence and global attractivity of positive periodic solution for a Volterra model with mutual interference and Beddington-DeAngelis functional response

In this paper, a Volterra model with mutual interference and Beddington-DeAngelis functional response is investigated, some sufficient conditions which guarantee the existence and global attractivity of positive periodic solution for the system are obtained. Furthermore, our results improve the main results of paper [1].     

A new predator-prey model with a profitless delay of digestion and impulsive perturbation on the prey

In this paper, we formulate a robust prey-dependent consumption predator-prey model with a delay of digestion and impulsive perturbation on the prey. Using the discrete dynamical system determined by the stroboscopic map, we obtain a ‘predator-eradication’ periodic solution and show that the ‘predator-eradication’ periodic solution is globally attractive when harvesting for the prey is over certain value. Using a new qualitative analysis method for impulsive and delay differential equations, we prove the system is uniformly persistent when harvesting for the prey is under certain value. Further, we show the delay of digestion is a “profitless” time delay. Moreover, we show our theoretical results by numerical simulation. In this paper, the main feature is that we introduce a delay of digestion and impulsive effects into the predator-prey model and exhibit a new mathematical method which is applied to investigate the system which is governed by both impulsive and delay differential equations.     

The asymptotic behavior of a nonautonomous eco-epidemic model with disease in the prey

A nonautonomous eco-epidemic model with disease in the prey is formulated and studied. Some sufficient and necessary conditions on the permanence and extinction of the infective prey are established by introducing the new research method. Some sufficient conditions on the global attractivity of the model are presented by constructing a Lyapunov function. Finally, an example is given to show that the periodic model is global attractivity if the infective prey is permanent.