A Review of Chaos Control Strategies for Tri-trophic Food Chain Ecological Systems
Keywords:food chain model, chaos control strategies, ecological systems, additional food, prey refuge, Allee effect, fear effect, species harvesting
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.
Authors who publish with Engineering Journal agree to transfer all copyright rights in and to the above work to the Engineering Journal (EJ)'s Editorial Board so that EJ's Editorial Board shall have the right to publish the work for nonprofit use in any media or form. In return, authors retain: (1) all proprietary rights other than copyright; (2) re-use of all or part of the above paper in their other work; (3) right to reproduce or authorize others to reproduce the above paper for authors' personal use or for company use if the source and EJ's copyright notice is indicated, and if the reproduction is not made for the purpose of sale.