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<p>This paper presents a comprehensive analysis of the bifurcation behavior of a two-dimensional predator-prey model described by a system of nonlinear difference equations. The study investigates the behavior of the system under different parameter regimes using both analytical and numerical techniques. Analytically, we employ a perturbation method to expand the system’s equations in a power series about the bifurcation point. This allows us to identify the types and scenarios of bifurcations that occur in the system, including period doubling, Neimark-Sacker, and strong resonance bifurcations. Numerical continuation methods implemented in MatcontM are used to validate the analytical results and gain further insights into the bifurcation structures.</p>

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Bifurcation Analysis of a Discrete-Time Prey-Predator Model: Theory and Numerical Continuation

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年5月26日

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  • Mohammadreza Mahmoudi,
  • Zohreh Eskandari

摘要

This paper presents a comprehensive analysis of the bifurcation behavior of a two-dimensional predator-prey model described by a system of nonlinear difference equations. The study investigates the behavior of the system under different parameter regimes using both analytical and numerical techniques. Analytically, we employ a perturbation method to expand the system’s equations in a power series about the bifurcation point. This allows us to identify the types and scenarios of bifurcations that occur in the system, including period doubling, Neimark-Sacker, and strong resonance bifurcations. Numerical continuation methods implemented in MatcontM are used to validate the analytical results and gain further insights into the bifurcation structures.