Permanence and Global Attractivity of a Discrete Logistic Model with Impulses

By piecewise Euler method, we construct a discrete logistic equation with impulses. The constructed model is more easily implemented at computer and is a better analogue of the continuous-time dynamic system. The dynamic behaviors of the constructed model are investigated. Sufficient conditions which guarantee the permanence and the global attractivity of positive solutions of the model are obtained. Numerical simulations show the feasibility of the main results

Dynamic Behaviors of Holling Type II Predator-Prey System with Mutual Interference and Impulses

A class of Holling type II predator-prey systems with mutual interference and impulses is presented. Sufficient conditions for the permanence, extinction, and global attractivity of system are obtained. The existence and uniqueness of positive periodic solution are also established. Numerical simulations are carried out to illustrate the theoretical results. Meanwhile, they indicate that dynamics of species are very sensitive with the period matching between species’ intrinsic disciplinarians and the perturbations from the variable environment. If the periods between individual growth and impulse perturbations match well, then the dynamics of species periodically change. If they mismatch each other, the dynamics differ from period to period until there is chaos

Population dynamical behavior of non-autonomous Lotka-Volterra competitive system with random perturbation

In this paper, we consider a non-autonomous stochastic Lotka-Volterra competitive system dxi(t) = xi(t)[(bi(t)¡ nPj=1aij (t)xj (t))dt+¾i(t)dBi(t)], where Bi(t) (i = 1; 2; ¢ ¢ ¢ ; n) are independent standard Brownian motions. Some dynamical properties are discussed and the su±cient conditions for the existence of global positive solutions, stochastic permanence, extinction as well as global attractivity are obtained. In addition, the limit of the average in time of the sample paths of solutions is estimated

On the Oscillation of the Generalized Food-Limited Equations with Delay

- The objective of the paper is to find conditions for the oscillation of the food-limited equation. We established conditions for the oscillation of all solutions of the generalized foodlimited equation by transforming the equation to a non-linear delay differential equation and then to a scalar delay differential equation and using the property of the scalar delay differential equation to obtain our result. Similarly we establish conditions for the oscillation of all solutions of the foodlimited equation with several delays by transforming the equation to a scalar differential equation to obtain the oscillatory property