Pattern formation induced by cross-diffusion in a predator--prey system

This paper considers the Holling--Tanner model for predator--preywith self and cross-diffusion. From the Turing theory, it isbelieved that there is no Turing pattern formation for the equalself-diffusion coefficients. However, combined with cross-diffusion,it shows that the system will exhibit spotted pattern by bothmathematical analysis and numerical simulations. Furthermore,asynchrony of the predator and the prey in the space. The obtainedresults show that cross-diffusion plays an important role on thepattern formation of the predator--prey system.