Influence of prey refuge on predator–prey dynamics

A diffusive predator–prey system with Michaelis–Menten type functional response subject to prey refuge is considered. Bifurcation analysis of Hopf and Turing are carried out in detail. In particular, Turing domain is given in the two parameters space. The obtained results show that the refuges used by prey have great influence on the pattern formation of the populations. More specifically, as prey refuge being increased, spotted pattern and coexistence of spotted and stripe-like pattern emerge. It is also proved that the pattern is not dependent on the initial conditions, which means the pattern is controlled by the intrinsic mechanism.