Global dynamics and integrability of a Leslie-Gower predator-prey model with linear functional response and generalist predator
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866917801946513408 |
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| author | Alvarez-Ramírez, Martha García-Saldaña, Johanna D. Medina, Mario |
| author_facet | Alvarez-Ramírez, Martha García-Saldaña, Johanna D. Medina, Mario |
| contents | We deal with a Leslie-Gower predator-prey model with a generalist or alternating food for predator and linear functional response. Using a topological equivalent polynomial system we prove that the system is not Liouvillian (hence also not Darboux) integrable. In order to study the global dynamics of this model, we use the Poincaré compactification of $\mathbb{R}^2$ to characterize all phase portraits in the Poincaré disc, obtaining two different topological phase portraits. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_10104 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Global dynamics and integrability of a Leslie-Gower predator-prey model with linear functional response and generalist predator Alvarez-Ramírez, Martha García-Saldaña, Johanna D. Medina, Mario Dynamical Systems Chaotic Dynamics 34A05, 34A34, 34C14, 34C20 We deal with a Leslie-Gower predator-prey model with a generalist or alternating food for predator and linear functional response. Using a topological equivalent polynomial system we prove that the system is not Liouvillian (hence also not Darboux) integrable. In order to study the global dynamics of this model, we use the Poincaré compactification of $\mathbb{R}^2$ to characterize all phase portraits in the Poincaré disc, obtaining two different topological phase portraits. |
| title | Global dynamics and integrability of a Leslie-Gower predator-prey model with linear functional response and generalist predator |
| topic | Dynamical Systems Chaotic Dynamics 34A05, 34A34, 34C14, 34C20 |
| url | https://arxiv.org/abs/2410.10104 |