Spatial memory drives spatiotemporal patterns in a predator-prey model describing intraguild predation

In this paper, we consider a predator-prey model describing intraguild predation with memory-based diffusion. We first investigate the stability of two semi-trivial constant steady states and find that they are unstable if the positive steady state exists and can not be stable at the same time. Then we study the stability of the positive constant steady state and find that system has no Turing bifurcation when the predator is assumed to forage the prey and multiple stability switches can arise through Hopf bifurcation with joint effects of the memory-based diffusion and delay. Numerical simulations also show that the competition between two consumers has also important influence on complex spatiotemporal patterns formation of system.