In this article we propose a unified framework in order to study reaction–diffusion systems containing self- and cross-diffusion using free energy approach. This naturally leads the formulation of an law, numerical method respecting discrete version latter. It constitutes alternative complements standard linear stability analysis, as it allows for nonlinear patterns, while monitoring evolution,...

In this paper we establish a general theoretical framework for Turing diffusion-driven instability for reaction-diffusion systems on time-dependent evolving domains. The main result is that Turing diffusion-driven instability for reaction-diffusion systems on evolving domains is characterised by Lyapunov exponents of the evolution family associated with the linearised system (obtained by linear...

Cross-diffusion, the phenomenon in which a gradient in the concentration of one species induces a flux of another chemical species, has generally been neglected in the study of reaction-diffusion systems. We summarize experiments that demonstrate that cross-diffusion coefficients can be quite significant, even exceeding "normal," diagonal diffusion coefficients in magnitude in systems that invo...