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.C., 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].

Pattern formation driven by cross–diffusion in a 2D domain

GAMBINO, Gaetana;LOMBARDO, Maria Carmela;SAMMARTINO, Marco Maria Luigi
2013-01-01

Abstract

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.C., 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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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/69743
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