Abstract
In this paper, we consider a predator-prey system with Holling type III ratio-dependent functional response. Such a system can exhibit complex dynamical behavior such as bistable and tristable phenomena which contain equilibria and oscillating motions for certain parameter values. In particular, we show that the ratio-dependent predator-prey system can exhibit multiple limit cycles due to Hopf bifurcation, giving rise to coexistence of stable equilibria and stable periodic solutions. These solutions may reveal some new type of patterns of complex dynamical behaviors in predator-prey systems.
| Original language | English |
|---|---|
| Article number | 2050129 |
| Journal | International Journal of Bifurcation and Chaos |
| Volume | 30 |
| Issue number | 9 |
| DOIs | |
| State | Published - Jul 1 2020 |
Keywords
- Holling type functional response
- Hopf bifurcation
- Predator-prey system
- bistable, tristable
- focus value
- limit cycle
- normal form