Complex spatiotemporal dynamics of a harvested prey–predator model with Crowley–Martin response function

The formation of spatiotemporal patterns is one of the most important part in the prey–predator dynamical system. In this paper, we investigate the local dynamics as well as the Turing structure through diffusion-driven instability by taking more general Crowley–Martin response function in the prey–predator system with the effect of linear harvesting of prey and predator. All the feasible equilibrium points are extracted. Boundedness, persistence, local and global stability, and Hopf bifurcation are established for some suitable parametric conditions. The parametric space for which the Turing spatial structure takes place is found out. Different kinds of patterns are demonstrated depending on the ecological parameters of the local system and diffusion coefficients.