Alejandro López-Nieto, Phillipo Lappicy, Nicola Vassena, Hannes Stuke, Jia-Yuan Dai
Published 2023-10-30, updated 2024-08-28Version 2
We describe a new mechanism that triggers periodic orbits in smooth dynamical systems. To this end, we introduce the concept of hybrid bifurcations: Such bifurcations occur when a line of equilibria with an exchange point of normal stability vanishes. Our main result is the existence and stability criteria of periodic orbits that bifurcate from breaking a line of equilibria. As an application, we obtain stable periodic coexistent solutions in an ecosystem for two competing predators with Holling's type II functional response.
Comments: Change of title from v1, typos corrected
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