Hopf periodic orbits for a ratio-dependent predator-prey model with stage structure
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 H...
| Authors: | , |
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| Format: | article |
| Publication Date: | 2016 |
| Country: | España |
| Institution: | Universitat Autònoma de Barcelona |
| Repository: | Dipòsit Digital de Documents de la UAB |
| Language: | English |
| OAI Identifier: | oai:ddd.uab.cat:169494 |
| Online Access: | https://ddd.uab.cat/record/169494 https://dx.doi.org/urn:doi:10.3934/dcdsb.2016026 |
| Access Level: | Open access |
| Keyword: | Averaging theory Hopf bifurcation Predator-prey model Ratio-dependence |
| Summary: | 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. |
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