Abstract
© 2017 John Wiley & Sons, Ltd. We prove that the Volterra-Gause system of predator-prey type exhibits 2 kinds of zero-Hopf bifurcations for convenient values of their parameters. In the first, 1 periodic solution bifurcates from a zero-Hopf equilibrium, and in the second, 4 periodic solutions bifurcate from another zero-Hopf equilibrium. This study is done using the averaging theory of second order.
| Original language | English |
|---|---|
| Pages (from-to) | 7858-7866 |
| Journal | Mathematical Methods in the Applied Sciences |
| Volume | 40 |
| Issue number | 18 |
| DOIs | |
| Publication status | Published - 1 Dec 2017 |
Keywords
- Periodic orbits
- Predator-prey system
- Volterra-Gause system
- Zero-Hopf bifurcation