Dynamic behaviors of a delay differential equation model of plankton allelopathy

作者：Chen Fengde^*; Li Zhong; Chen Xiaoxing; Laitochova Jitka

来源：Journal of Computational and Applied Mathematics, 2007, 206(2): 733-754.

DOI：10.1016/j.cam.2006.08.020

• competition
• toxicology
• Lyapunov functional
• global attractivity
• permanence
• extinction

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.

• 出版日期2007-9-15
• 单位福州大学