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<p>Predator-prey interactions are fundamental to ecological systems, often exhibiting nonlinear and complex behaviors. The classical Rosenzweig-MacArthur (RMA) model has been instrumental in understanding these dynamics, but real-world ecosystems often involve higher trophic interactions. In this study, we modify the classical RMA model by incorporating a&#xa0;super-predator, extending it into a&#xa0;discrete-time three-species framework. This modification introduces additional complexity, leading to richer dynamical behaviors, including high-period oscillations and chaotic dynamics. We perform a&#xa0;rigorous local stability analysis of equilibrium points and examine the emergence of bifurcations, particularly Neimark-Sacker (NS) bifurcations, which indicate transitions to quasi-periodic and chaotic dynamics. Numerical simulations demonstrate that variations in interaction rates, particularly prey-predator (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\beta\)</EquationSource> </InlineEquation>) and prey-super-predator (<InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\theta\)</EquationSource> </InlineEquation>), significantly influence system stability and dynamical behavior. Our findings reveal that controlled parameter adjustments can regulate bifurcations and prevent undesirable population fluctuations, offering practical implications for ecological management and conservation strategies. These results contribute to a&#xa0;deeper understanding of how multi-trophic interactions shape ecosystem stability and complexity in discrete-time predator-prey models.</p>

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Nonlinear Dynamics and Bifurcation Analysis in a Modified Discrete-Time Rosenzweig-MacArthur Predator-Prey Model

  • 期刊论文

  • 发表日期：

    2025年9月5日

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  • Sujay Goldar,
  • Purnendu Sardar,
  • Santosh Biswas,
  • Sk Sarif Hassan,
  • Rasmikanta Pati,
  • Ahmed A. Mohsen,
  • Krishna Pada Das

摘要

Predator-prey interactions are fundamental to ecological systems, often exhibiting nonlinear and complex behaviors. The classical Rosenzweig-MacArthur (RMA) model has been instrumental in understanding these dynamics, but real-world ecosystems often involve higher trophic interactions. In this study, we modify the classical RMA model by incorporating a super-predator, extending it into a discrete-time three-species framework. This modification introduces additional complexity, leading to richer dynamical behaviors, including high-period oscillations and chaotic dynamics. We perform a rigorous local stability analysis of equilibrium points and examine the emergence of bifurcations, particularly Neimark-Sacker (NS) bifurcations, which indicate transitions to quasi-periodic and chaotic dynamics. Numerical simulations demonstrate that variations in interaction rates, particularly prey-predator ( \(\beta\) ) and prey-super-predator ( \(\theta\) ), significantly influence system stability and dynamical behavior. Our findings reveal that controlled parameter adjustments can regulate bifurcations and prevent undesirable population fluctuations, offering practical implications for ecological management and conservation strategies. These results contribute to a deeper understanding of how multi-trophic interactions shape ecosystem stability and complexity in discrete-time predator-prey models.