Nonlinear dynamics and chaos control of a discrete Rosenzweig-MacArthur prey-predator model - Bouguettoucha, Teqwa; Boukhalfa, Nadjla; Abdelouahab, Mohammed Salah (Journal of Innovative Applied Mathematics and Computational Sciences, 2025)
This paper investigates the nonlinear dynamics and chaos control of a discrete Rosenzweig-MacArthur predator-prey model. We first conduct a thorough dynamical analysis, identifying the system's equilibrium points and examining their stability conditions. The study reveals the occurrence of Flip and Neimark-Sacker bifurcations, which represent critical qualitative changes in population dynamics. Specifically, Flip bifurcations lead to period-doubling phenomena, while Neimark-Sacker bifurcations indicate the emergence of quasi-periodic oscillations, both of which are crucial for understanding the onset of complex behaviors such as cycles and oscillations in ecological systems. To address the chaotic dynamics induced by these bifurcations, two control strategies are applied: the Ott-Grebogi-Yorke (OGY) method and feedback control. The results demonstrate the effectiveness of both approaches in stabilizing the system's dynamics, with the OGY method proving to be more effective in achieving faster stabilization. These findings provide valuable insights into the management and preservation of ecological systems where predator-prey interactions exhibit instability and chaos.