A Review of Chaos Control Strategies for Tri-trophic Food Chain Ecological Systems

Abstract

. The existence of chaos in ecological models is quite obvious due to the presence of nonlinear terms. Controlling chaotic phenomena in ecological systems remains a difficult task due to their unpredictability, and thus chaos control is one of the main objectives for constructing mathematical models in ecology today. Our aim in this paper is to review chaos control strategies for the tri-trophic food chain models by using various ecological factors. The factors include additional food, prey refuge, the Allee effect, the fear effect, and harvesting. We establish the essential conditions for the existence of ecologically feasible equilibrium points in the food chain ecological systems and their local stability. This paper provides a unified overview of recent research on the chaos control of ecological systems. The theoretical results suggest a way to control populations of species in ecological systems for fishing and pest management in farming. Numerical examples are performed to justify and compare the theoretical findings through phase portraits and bifurcation diagrams.