Cross-diffusion effects on stationary pattern formation in the FitzHugh-Nagumo model

<p style='text-indent:20px;'>We investigate the formation of stationary patterns in FitzHugh-Nagumo reaction-diffusion system with linear cross-diffusion terms. We focus our analysis on effects Turing mechanism. Linear stability indicates that positive values inhibitor enlarge region parameter space where a instability is excited. A sufficiently large coefficient removes requirement imposed by classical mechanism must diffuse faster than activator. In an extended new phenomenon occurs, namely existence double bifurcation threshold inhibitor/activator diffusivity ratio for onset patterning instabilities: ratio, emerge two species are in-phase, while, small diffusion predicts out-of-phase spatial structures (named <i>cross-Turing patterns</i>). addition, increasingly cross-diffusion, upper and lower thresholds merge, so develops independently value whose magnitude selects or cross-Turing patterns. Finally, pattern selection problem addressed through weakly nonlinear analysis.</p>