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<p>We describe a new mechanism that triggers periodic orbits in smooth dynamical systems. To this end, we introduce the concept of hybrid bifurcations, which consists of a bifurcation without parameters and a classical bifurcation. Our main result classifies the hybrid bifurcation when a line of equilibria with an exchange point of normal stability vanishes. We showcase the efficacy of our approach by proving stable periodic coexistent solutions in an ecosystem of two competing predators with Holling’s type II functional response.</p>

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Hybrid bifurcations: periodicity from eliminating a line of equilibria

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年1月7日

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  • Alejandro López-Nieto,
  • Phillipo Lappicy,
  • Nicola Vassena,
  • Hannes Stuke,
  • Jia-Yuan Dai

摘要

We describe a new mechanism that triggers periodic orbits in smooth dynamical systems. To this end, we introduce the concept of hybrid bifurcations, which consists of a bifurcation without parameters and a classical bifurcation. Our main result classifies the hybrid bifurcation when a line of equilibria with an exchange point of normal stability vanishes. We showcase the efficacy of our approach by proving stable periodic coexistent solutions in an ecosystem of two competing predators with Holling’s type II functional response.