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<p>Ecological systems are often subject to time-dependent environmental influences, which can significantly impact their stability and long-term behavior. This study examines the dynamics of a quasiperiodically forced Hassell map, focusing on the existence and breakdown of invariant curves under environmental fluctuations. Through theoretical analysis and numerical simulations, we identify conditions under which invariant curves undergo bifurcations, leading to their breakdown and the emergence of strange nonchaotic attractors (SNAs). The transition to SNAs occurs via multiple routes, including torus-doubling, fractalization, and interior crisis. A detailed investigation of saddle-node bifurcations in periodic orbits reveals their crucial role in the destruction of smooth invariant curves. These mechanisms help explain how environmental variability can lead to critical transitions in ecological populations, even in the absence of traditional chaotic dynamics.</p>

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Stability and bifurcation in an ecological system under time-dependent environmental influences

  • 期刊论文

  • 发表日期：

    2025年7月17日

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  • Yiwen Chen,
  • Jicheng Duan,
  • Denghui Li,
  • Gaolei Li

摘要

Ecological systems are often subject to time-dependent environmental influences, which can significantly impact their stability and long-term behavior. This study examines the dynamics of a quasiperiodically forced Hassell map, focusing on the existence and breakdown of invariant curves under environmental fluctuations. Through theoretical analysis and numerical simulations, we identify conditions under which invariant curves undergo bifurcations, leading to their breakdown and the emergence of strange nonchaotic attractors (SNAs). The transition to SNAs occurs via multiple routes, including torus-doubling, fractalization, and interior crisis. A detailed investigation of saddle-node bifurcations in periodic orbits reveals their crucial role in the destruction of smooth invariant curves. These mechanisms help explain how environmental variability can lead to critical transitions in ecological populations, even in the absence of traditional chaotic dynamics.