Home > Articles > Published articles > Hopf periodic orbits for a ratio-dependent predator-prey model with stage structure |
Date: | 2016 |
Abstract: | A ratio-dependent predator-prey model with stage structure for prey was investigated in [8]. There the authors mentioned that they were unable to show if such a model admits limit cycles when the unique equilibrium point E ∗ at the positive octant is unstable. Here we characterize the existence of Hopf bifurcations for the systems. In particular we provide a positive answer to the above question showing for such models the existence of small-amplitude Hopf limit cycles being the equilibrium point E ∗ unstable. |
Grants: | Ministerio de Educación y Ciencia MTM2013-40998-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-568 European Commission 316338 European Commission 316339 |
Note: | Agraïments: The second author is partially supported by Dirección de Investigación DIUBB 1204084/R. |
Rights: | Tots els drets reservats. |
Language: | Anglès |
Document: | Article ; recerca ; Versió acceptada per publicar |
Subject: | Averaging theory ; Hopf bifurcation ; Predator-prey model ; Ratio-dependence |
Published in: | Discrete and continuous dynamical systems. Series B, Vol. 21 Núm. 6 (2016) , p. 1859-1867, ISSN 1553-524X |
Postprint 9 p, 334.3 KB |