Spatiotemporal complexity of a predator–prey system with constant harvest rate

In this paper, we investigate the emergence of a predator–prey system with Michaelis–Menten-type predator–prey systems with reaction–diffusion and constant harvest rate. We derive the conditions for Hopf and Turing bifurcation on the spatial domain. The results of spatial pattern analysis, via numerical simulations, typical spatial pattern formation is isolated groups, i.e., stripe-like, patch-like and so on. Our results show that modeling by reaction–diffusion equations is an appropriate tool for investigating fundamental mechanisms of complex spatiotemporal dynamics. It will be useful for studying the dynamic complexity of ecosystems.