1211.4412 (G. Gambino et al.)

Pattern formation driven by cross--diffusion in a 2D domain    [PDF]

G. Gambino, M. C. Lombardo, M. Sammartino

In this work we investigate the process of pattern formation in a two dimensional domain for a reaction-diffusion system with nonlinear diffusion terms and the competitive Lotka-Volterra kinetics. The linear stability analysis shows that cross-diffusion, through Turing bifurcation, is the key mechanism for the formation of spatial patterns. We show that the bifurcation can be regular, degenerate non-resonant and resonant. We use multiple scales expansions to derive the amplitude equations appropriate for each case and show that the system supports patterns like rolls, squares, mixed-mode patterns, supersquares, hexagonal patterns.

View original: http://arxiv.org/abs/1211.4412