Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
837582 | Nonlinear Analysis: Real World Applications | 2013 | 25 Pages |
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.
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Authors
G. Gambino, M.C. Lombardo, M. Sammartino,