Dynamic behaviors of a delay differential equation model of plankton allelopathy

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:206

Article

Chen, Fengde ; Li, Zhong ; Chen, Xiaoxing ; Laitochova, Jitka

关键词: competition;    toxicology;    Lyapunov functional;    global attractivity;    permanence;    extinction;   

DOI  :  10.1016/j.cam.2006.08.020

来源: Elsevier

【 摘 要 】

In this paper, we consider a modified delay differential equation model of the growth of n-species of plankton having competitive and allelopathic effects on each other. We first obtain the sufficient conditions which guarantee the permanence of the system. As a corollary, for periodic case, we obtain a set of delay-dependent condition which ensures the existence of at least one positive periodic solution of the system. After that, by means of a suitable Lyapunov functional, sufficient conditions are derived for the global attractivity of the system. For the two-dimensional case, under some suitable assumptions, we prove that one of the components will be driven to extinction while the other will stabilize at a certain solution of a logistic equation. Examples show the feasibility of the main results. (C) 2006 Elsevier B.V. All rights reserved.

【 授权许可】

Free