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.
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 [10.1016/j.nonrwa.2012.11.009].
Data di pubblicazione: | 2013 | |
Titolo: | Pattern formation driven by cross–diffusion in a 2D domain | |
Autori: | ||
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 [10.1016/j.nonrwa.2012.11.009]. | |
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Digital Object Identifier (DOI): | http://dx.doi.org/10.1016/j.nonrwa.2012.11.009 | |
Appare nelle tipologie: | 1.01 Articolo in rivista |
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