Exploring Neimark-Sacker Bifurcation and Chaos Control in a Tri-species Discrete-Time Model

Abstract

This article presents a three-dimensional discrete-time ecological model to elucidate the intricate dynamics among three distinct species within an ecosystem. This approach extends traditional two-dimensional models, offering a more comprehensive perspective on ecological interactions. We identify all biologically feasible equilibria and perform a local stability analysis for each equilibrium point. Through bifurcation analysis (Neimark-Sacker and period-doubling bifurcations), we successfully demonstrate chaotic attractors via period doubling in the discrete-time model and implement chaos control through numerical simulations. By integrating this mathematical model, we derive ecological insights that contribute to informed conservation and management strategies, promoting sustainable biodiversity preservation.