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Dynamical transitions and chaos control in a discrete predator–prey model with Gompertz growth and Holling type III response

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  • Almatrafi, M.B.
  • Berkal, Messaoud
  • Ahmed, Rizwan

Abstract

This study investigates the dynamics of a discrete predator–prey model derived from a continuous system using the forward Euler method. The model features Gompertz growth for the prey and a Holling type III functional response for the predator. We analyze the existence and local stability of equilibria and identify conditions under which the system exhibits period-doubling and Neimark–Sacker bifurcations, marking the onset of oscillatory and complex dynamics. To detect chaos, we apply the 0−1 chaos test, confirming irregular behavior in specific parameter regimes. Numerical simulations, including bifurcation diagrams, Lyapunov exponents, phase portraits, and time series plots, demonstrate the model’s rich dynamical behavior. Two control strategies, hybrid control and state feedback control, are implemented to control bifurcation and chaos. Our findings highlight how nonlinear responses and discrete-time dynamics can generate unpredictable population patterns and provide tools for stabilizing ecological systems.

Suggested Citation

  • Almatrafi, M.B. & Berkal, Messaoud & Ahmed, Rizwan, 2025. "Dynamical transitions and chaos control in a discrete predator–prey model with Gompertz growth and Holling type III response," Chaos, Solitons & Fractals, Elsevier, vol. 200(P2).
    • Handle: RePEc:eee:chsofr:v:200:y:2025:i:p2:s0960077925010847
    DOI: 10.1016/j.chaos.2025.117071
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