Pattern formation in a ratio-dependent predator-prey model with cross-diffusion

In this paper, a ratio-dependent predator-prey model with cross-diffusion is studied. By the linear stability analysis, the necessary conditions for the occurrence of Turing instability are obtained. Moreover, the amplitude equations for the excited modes are gained by means of weakly nonlinear analysis. Numerical simulations are presented to verify the theoretical results and show that the cross-diffusion plays an important role in the pattern formation.