A ratio-dependent predator-prey model with stage structure for prey was investigated in . 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.
|Journal||Discrete and Continuous Dynamical Systems - Series B|
|Publication status||Published - 1 Aug 2016|
- Averaging theory
- Hopf bifurcation
- Predator-prey model