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<p>In this work, we investigate a discrete-time Bazykin–Berezovskaya predator–prey model incorporating density-proportional immigration. Using bifurcation-theoretic analysis, we characterize codimension-1 bifurcations, including transcritical, period-doubling, and Neimark–Sacker bifurcations, as well as codimension-2 bifurcations such as 1:2 and 1:4 strong resonances arising from immigration-growth-Allee effect interactions. Numerical continuation reveals that controlled immigration enhances coexistence stability by suppressing oscillatory regimes while preserving bistability. The interplay between immigration rates, intrinsic growth dynamics, and the strong Allee effect establishes critical thresholds for immigration that ensure population persistence, mitigate oscillatory instabilities, and promote long-term coexistence in discrete-time predator–prey systems.</p>

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Exploring multi-parameter bifurcations and immigrationdriven dynamics in a discrete-time Bazykin–Berezovskaya prey–predator model

  • 期刊论文

  • 发表日期：

    2025年10月1日

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  • Hajar Mouhsine,
  • Karima Mokni,
  • Mohamed Ch-Chaoui

摘要

In this work, we investigate a discrete-time Bazykin–Berezovskaya predator–prey model incorporating density-proportional immigration. Using bifurcation-theoretic analysis, we characterize codimension-1 bifurcations, including transcritical, period-doubling, and Neimark–Sacker bifurcations, as well as codimension-2 bifurcations such as 1:2 and 1:4 strong resonances arising from immigration-growth-Allee effect interactions. Numerical continuation reveals that controlled immigration enhances coexistence stability by suppressing oscillatory regimes while preserving bistability. The interplay between immigration rates, intrinsic growth dynamics, and the strong Allee effect establishes critical thresholds for immigration that ensure population persistence, mitigate oscillatory instabilities, and promote long-term coexistence in discrete-time predator–prey systems.