Delay-driven spatial patterns in a predator-prey model with constant prey harvesting

This paper deals with a predator-prey model with time delay and constant prey harvesting. We investigate the effect of the time delay on the stability of the coexistence equilibrium and demonstrate that time delay can induce spatial patterns. Furthermore, a Hopf bifurcation occurs when the delay increases to a critical value. By applying normal form theory and the center manifold theorem, we develop the explicit formulae that determines the stability and direction of the bifurcating periodic solutions. Finally, we show how the initial condition affects the types of spatial patterns by numerical simulations.