Dynamical complexity in a discrete tri-trophic Rosenzweig–MacArthur system: Bifurcations, chaos and hybrid control

Sujay Goldar

Chaos, Solitons & Fractals, 2025, vol. 201, issue P1

Abstract: We study the dynamical behavior of a discrete-time tri-trophic Rosenzweig–MacArthur predator–prey model with a superpredator. The continuous-time model is discretized using piecewise constant arguments to reflect non-overlapping generations and abrupt ecological interactions. We analyze the existence and stability of equilibria and derive conditions for local asymptotic stability and bifurcations, including transcritical, Neimark–Sacker, and period-doubling types, using Jury criterion and characteristic polynomial techniques. Numerical simulations demonstrate rich dynamics ranging from stable equilibria to high-period oscillations and chaos, showing that the discrete-time system exhibits greater complexity than its continuous counterpart. A hybrid control strategy that combines state feedback with parameter perturbation is proposed to suppress chaos while preserving ecological realism. The findings highlight the role of superpredators in shaping ecosystem stability and provide insights relevant to ecological forecasting, conservation, and pest management.

Keywords: Rosenzweig–MacArthur; Discrete-time dynamics; Bifurcation analysis; Chaos control; Tri-trophic interactions (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:201:y:2025:i:p1:s0960077925012470

DOI: 10.1016/j.chaos.2025.117234

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