Stability, Hopf bifurcations and spatial patterns in a delayed diffusive predator-prey model with herd behavior

作者：Tang, Xiaosong; Song, Yongli^*

来源：Applied Mathematics and Computation, 2015, 254: 375-391.

DOI：10.1016/j.amc.2014.12.143

• Predator-prey model
• Herd behavior
• Delay
• Diffusion
• Hopf bifurcation
• Pattern formation

In this paper, we consider a delayed diffusive predator-prey model with herd behavior. Firstly, by choosing the appropriate bifurcation parameter, the stability of the positive equilibria and the existence of Hopf bifurcations, induced by diffusion and delay respectively, are investigated by analyzing the corresponding characteristic equation. 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. Furthermore, the instability of the Hopf bifurcation leads to the emergence of spatial patterns. Finally, some numerical simulations are also carried out to illustrate and expand the theoretical results.

• 出版日期2015-3-1
• 单位井冈山大学; 同济大学