Validating Numerical to Theoretical Solutions in a \Reaction-Diffusion with Linear Cross-Diffusion Systems.

In tliis paper, we consider a reaction diffusion system with linear cross-diffusion. We carry‘out the analytical study in detail and find out that, when the diffusion coefficient is unity, Turing instability does not occur, but with the introduction of cross-diffusion, the system exhibit Turing instability. The numerical results reveal that, on increasing the value of, there is an occurrence of spatial patterns which conforms with the theoretical results. The cross-diffusion coefficients really play a vitaj role on the parameter spaces and spatial patterns of our system,