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, and hexagonal patterns.
|Data di pubblicazione:||2013|
|Titolo:||Pattern formation driven by cross–diffusion in a 2D domain|
|Citazione:||Gambino, G., Lombardo, M., & Sammartino, M. (2013). Pattern formation driven by cross–diffusion in a 2D domain. NONLINEAR ANALYSIS: REAL WORLD APPLICATIONS, 14 (3), 1755-1779.|
|Digital Object Identifier (DOI):||10.1016/j.nonrwa.2012.11.009|
|Appare nelle tipologie:||1.01 Articolo in rivista|