Pattern formation driven by cross-diffusion in a 2D domain |
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Authors: | G Gambino MC Lombardo M Sammartino |
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Institution: | University of Palermo, Department of Mathematics, Via Archirafi 34, 90123 Palermo, Italy |
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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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