Dynamics of three species plankton model with Holling type-IV functional responses and control of toxic phytoplankton

Abstract

In this paper we proposed a minimal model of non-toxic phytoplankton - toxic phytoplankton - zooplankton dynamics with Holling type-II and Holling type-IV functional responses. We carried out the analytical study of spatial and non-spatial model for one dimensional system in detail and found out the condition for diffusive instability of a locally stable equilibrium. With the help of numerical simulations, we have observed that when the rate of inhibition of zooplankton growth by toxic material ingested in feeding on toxic phytoplankton is very large, then because of high toxic effect, the zooplankton goes to extinction.

Keywords

• plankton
• planktonic bloom
• diffusion
• spatio-temporal pattern