Pattern transitions in a vegetation system with cross-diffusion

Regular pattern is a typical feature of vegetation distribution which can be recognized as early warnings of desertification. In this work, a vegetation system with cross diffusion is presented based on reaction-diffusion equations. By means of mathematical analysis, we obtain the appropriate parameter space which can ensure the emergence of stationary patterns. Moreover, it is unveiled that cross diffusion not only induces the pattern transitions, yet promotes the density of the vegetation. These obtained results suggest that cross diffusion is an important mechanism in vegetation dynamics.