Spatial-Temporal Patterns Induced by Time Delay and Taxis in a Predator–Prey System

Time delays and taxi effects are important factors in the predator–prey interaction. This paper focuses on calculating the normal form on the center manifold near the Hopf bifurcation point for a general delayed diffusive predator–prey system with taxis under the Neumann boundary condition. A delayed diffusive Lotka–Volterra predator–prey model with prey-taxis is considered as an application. By numerical simulations, in the two-parameter plane, different types of spatial-temporal patterns are observed by varying delay or taxis.