Extinction of a delay differential equation model of plankton allelopathy

Abstract

In this paper, a delay differential equation model of the growth of two-species competitive plankton with one toxin producing phytoplankton is studied in this paper. Under some suitable assumption, we prove that one of the components will be driven to extinction while the other one will stabilize at a certain solution of a Logistic equation. Our results supplement one of the main results in [Dynamic behaviors of a delay differential equation model of plankton allelopathy, J. Comput. Appl. Math. 206 (2007), 733-754].