Dynamic behaviors of a delay differential equation model of plankton allelopathy

By Fengde Chen, Zhong Li, Xiaoxing Chen, J. Laitochová. 2007

61 citations recorded by the source corpus.

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.

Subfields: Genetics, Global and Planetary Change, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/c5e8dce82ce610d5a214c1f933904b7716726a87

Citations in the corpus

• Mathematical analysis and numerical simulation of pattern formation under cross-diffusion (2013, unknown): “[42] studied the effects of time-delay on equilibrium stability and Hopf bifurcation, and additionally Liu et al.”