Modelling the Effects of Competing Toxin Producing Phytoplankton on a Zooplankton Population: Role of Holling Type-II Functional Response with Time-Lag

Abstract

In this paper, a system consisting of two competing harmfu l phytoplankton and a zooplankton with Holling type-II functional response and discrete time lag is considered. A stable co-existence of all the species has been observed for the system without delay and the Hopf-b ifurcation phenomenon is observed for the interior equilibriu m po int. The Hopf-bifurcating solution is obtained for the critical values of parameters like predation rates and half saturation constants. Further, using the normal form theory, we have determined the direction and the stability of the Hopf-bifurcation solution. The introduction of time delay in the system also shows the Hopf-bifurcat ion as the delay parameter passes through a critical value. Finally, the numerical simu lation is carried out to support the theoretical results.