Dynamics of Gilpin-ayala Competition Model with Random Perturbation

Schoener's model and Drosophila competition.

Schoener (1973) has recently discussed a simple model of growth and competition. It is one that we did not include in the list of models we (Ayala, Gilpin and Ehrenfeld, 1973; Gilpin and Ayala, 1973), fitted to data on interspecies competition between Drosophila willistoni and D. pseudoobscura. Since we were striving there for completeness, we should like in this note to treat Schoener’s model ...

Positive Periodic Solutions of A Generalized Gilpin-Ayala Competitive System With Time Delays

Abstract: In this paper, we investigate a generalized Gilpin-Ayala competition system which is more general and more realistic than the classical Lotka-Volterra competition system. By the fixed-point theorem and differential mean value, some sufficient conditions guaranteeing the existence, uniqueness and exponential stability of positive periodic solutions for a generalized Gilpin-Ayala compet...

Dynamics of stochastic hybrid Gilpin-Ayala system with impulsive perturbations

This paper is mainly concerned with the dynamics of the stochastic Gilpin-Ayala model under regime switching with impulsive perturbations. The goal is to analyze the effects of Markov chain and impulse on the dynamics. Some asymptotic properties are considered and sufficient criteria for stochastic permanence, extinction, non-persistence in the mean and weak persistence are obtained. The critic...

Asymptotic Behavior of Stochastic Gilpin-ayala Mutualism Model with Jumps

This article concerns the study of stochastic Gilpin-Ayala mutualism models with white noise and Poisson jumps. Firstly, an explicit solution for one-dimensional Gilpin-Ayala mutualism model with jumps is obtained and the asymptotic pathwise behavior is analyzed. Then, sufficient conditions for the existence of global positive solutions, stochastically ultimate boundedness and stochastic perman...

Multiple positive periodic solutions for a food-limited two-species Gilpin-Ayala competition patch system with periodic harvesting terms