Exploring chaos and bifurcation in a discrete prey–predator based on coupled logistic map

Abstract

Abstract This research paper investigates discrete predator-prey dynamics with two logistic maps. The study extensively examines various aspects of the system’s behavior. Firstly, it thoroughly investigates the existence and stability of fixed points within the system. We explores the emergence of transcritical bifurcations, period-doubling bifurcations, and Neimark-Sacker bifurcations that arise from coexisting positive fixed points. By employing central bifurcation theory and bifurcation theory techniques. Chaotic behavior is analyzed using Marotto’s approach. The OGY feedback control method is implemented to control chaos. Theoretical findings are validated through numerical simulations.

Keywords

• Coupled-logistic map
• Predator–prey model
• Stability
• Bifurcation
• Marotto’s map
• Chaos