The Dynamics of the Aquatic Food Chain System in the Contaminated Environment

Abstract

In this paper, the aquatic food chain model, consisting of Phytoplankton, Zooplankton, and Fish, in the contaminated environment is proposed and studied. Modified Leslie-Gower model with Holling type IV functional response are used to describe the growth of Fish and the food transition throughout the food chain, respectively. The toxic substance affects directly the Phytoplankton and indirectly the other species. The local stability analysis of all possible equilibrium points is done. The persistence conditions of the model are established. The basin of attraction for each point is specified using the Lyapunov function. Bifurcation analysis near the coexistence equilibrium point is investigated. Detecting the existence of chaos is carried out using bifurcation diagrams. Numerical simulation shows that the food chain has rich dynamics including chaos. Moreover, the existence of toxic substances works as a stabilizing factor in the model.