The consequences of pollution on the producer-consumer-predator food chain dynamics when the predator has access to extra food

Abstract

It is known that pollution can have significant consequences on the dynamics of the producer-consumer-predator food chain, especially when predators have access to extra food sources due to the impact of pollution on environmental resources. Consequently, this paper proposes and investigates a novel mathematical model of the food chain that involves Producer-Consumer-Predator with extra food sources for a predator in a polluted environment. All the solution properties are discussed. The equilibrium points are determined along with their local stability conditions. Lyapunov functions are proposed to discuss the possibility of global stability. The concentrates at which the system undergoes persistence are found. Local bifurcation analysis is carried out to understand the influence of parameters on the dynamics of the system. A numerical simulation of the system is applied to confirm the analytic findings.