Turing pattern formation in a fractional-order reaction-diffusion Holling-IV predator-prey model

It is well known that there is nonexistence of Turing instability in the integer-order Holling type-IV reaction-diffusion predator-prey model. In this paper, we investigate the spatiotemporal dynamics of the effect of the fractional-order derivative and diffusion on the reaction-diffusion predator-prey model with Holling type-IV functional response. Additionally, we give the conditions that Turing instability occurs in the model, which is induced by the fractional-order and diffusion together. Via numerical simulations, we present the evolutionary processes that involve organism distribution and the interaction of spatially distributed prey with local diffusion, and find that the model dynamics exhibits rich and complex Turing patterns.