2012/11/19 by G. Gambino, M. C. Lombardo, M. Sammartino · 1 citation
Physics and Astronomy · Mathematics · #nlin.PS #math-ph #math.DS #math.MP
paper · pdf · doi:10.1016/j.nonrwa.2012.11.009
published as Nonlinear Analysis: Real World Applications, 14 (3) , pp. 1755-1779 , (2013)
arxiv created 2012/11/19 · arxiv updated 2014/03/03
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.