| Volume 7, Number 4, 2017, Pages 1385-1401 DOI：10.11948/2017084 |
| Delay induced subcritical Hopf bifurcation in a diffusive predator-prey model with herd behavior and hyperbolic mortality |
| Xiaosong Tang,Heping Jiang,Zhiyun Deng,Tao Yu |
| Keywords:Predator-prey model with herd behavior, hyperbolic mortality, delay, diffusion, Hopf bifurcation, periodic solutions. |
| Abstract: |
| In this paper, we consider the dynamics of a delayed diffusive predator-prey model with herd behavior and hyperbolic mortality under Neumann boundary conditions. Firstly, by analyzing the characteristic equations in detail and taking the delay as a bifurcation parameter, the stability
of the positive equilibria and the existence of Hopf bifurcations induced by delay are investigated. Then, applying the normal form theory and the center manifold argument for partial functional differential equations, the formula determining the properties of the Hopf bifurcation are obtained. Finally, some numerical simulations are also carried out and we obtain the unstable spatial periodic solutions, which are induced by the subcritical Hopf bifurcation. |
PDF Download reader
|
|
|
|