Hybrid Bifurcations: Periodicity from Eliminating a Line of Equilibria

Hybrid Bifurcations: Periodicity from Eliminating a Line of Equilibria

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 c...

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Veröffentlicht in:arXiv.org 2024-08
Hauptverfasser: López-Nieto, Alejandro, Lappicy, Phillipo, Vassena, Nicola, Stuke, Hannes, Jia-Yuan, Dai
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Bifurcations
Orbits
Predators
Stability criteria
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creator López-Nieto, Alejandro
Lappicy, Phillipo
Vassena, Nicola
Stuke, Hannes
Jia-Yuan, Dai
description 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.
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subjects Bifurcations
Orbits
Predators
Stability criteria
title Hybrid Bifurcations: Periodicity from Eliminating a Line of Equilibria
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