Zero-Hopf bifurcation in a predator-prey model
We study the competition between two species according the following modification of the Holling-Tanner II model x'= x[r(1 -x/K)-qy/x2 + a], y' = sy (1 -y/nx + c). Of course, x ≥ 0, y ≥ 0 and the parameters a, c, K, n, q, r and s are positive. We prove that its unique positive equilibrium...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2013 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:150570 |
| Acceso en línea: | https://ddd.uab.cat/record/150570 |
| Access Level: | acceso abierto |
| Palabra clave: | Zero-Hopf bifurcation Predator-prey model |
| Sumario: | We study the competition between two species according the following modification of the Holling-Tanner II model x'= x[r(1 -x/K)-qy/x2 + a], y' = sy (1 -y/nx + c). Of course, x ≥ 0, y ≥ 0 and the parameters a, c, K, n, q, r and s are positive. We prove that its unique positive equilibrium point never exhibits a classical Hopf bifurcation, but for convenient values of the parameters from this equilibrium point bifurcates a periodic orbit, and during this local bifurcation the eigenvalues of such equilibrium remain purely imaginary. |
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