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.
| Original language | English |
|---|---|
| Pages (from-to) | 1859-1867 |
| Journal | Discrete and Continuous Dynamical Systems - Series B |
| Volume | 21 |
| Issue number | 6 |
| DOIs | |
| Publication status | Published - 1 Aug 2016 |
Keywords
- Averaging theory
- Hopf bifurcation
- Predator-prey model
- Ratio-dependence