Hybrid Bifurcations: Periodicity from Eliminating a Line of Equilibria
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866929662055153664 |
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| author | López-Nieto, Alejandro Lappicy, Phillipo Vassena, Nicola Stuke, Hannes Dai, Jia-Yuan |
| author_facet | López-Nieto, Alejandro Lappicy, Phillipo Vassena, Nicola Stuke, Hannes Dai, Jia-Yuan |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2310_19604 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Hybrid Bifurcations: Periodicity from Eliminating a Line of Equilibria López-Nieto, Alejandro Lappicy, Phillipo Vassena, Nicola Stuke, Hannes Dai, Jia-Yuan Dynamical Systems Classical Analysis and ODEs 34C20, 34C25, 34D20, 37G10, 37J40, 92D25 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. |
| title | Hybrid Bifurcations: Periodicity from Eliminating a Line of Equilibria |
| topic | Dynamical Systems Classical Analysis and ODEs 34C20, 34C25, 34D20, 37G10, 37J40, 92D25 |
| url | https://arxiv.org/abs/2310.19604 |