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

摘要: In this paper, we consider a delayed diffusive predator-prey model with herd behavior. Firstly, by choosing the appropriate bifurcation parameter, stability of positive equilibria and existence Hopf bifurcations, induced diffusion delay respectively, are investigated analyzing corresponding characteristic equation. Then, applying normal form theory center manifold argument for partial functional differential equations, formula determining properties obtained. Furthermore, instability leads to emergence spatial patterns. Finally, some numerical simulations also carried out illustrate expand theoretical results.