Turing instability in a gene network with cross-diffusion

In this paper, we consider the process of pattern formation induced by nonlinear diffusion in the gene network with cross-diffusion. We present a theoretical analysis of the pattern formation and show how cross-diffusion is able to destabilize the uniform equilibrium, being therefore liable for the emergence of spatial patterns. Through the linear stability analysis, we analytically derive a set of sufficient conditions which guarantee that the system generates turing instability, indicating that the competition and cross-diffusion between protein and mir-17-92 can lead to the turing pattern formation. Furthermore, we also obtain the Turing regions in which Turing patterns are generated.