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

G. Gambino; M. C. Lombardo; M. Sammartino

doi:10.1016/j.nonrwa.2012.11.009

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arXiv · 1211.4412

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

G. Gambino·M. C. Lombardo·M. Sammartino

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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, hexagonal patterns.

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G. Gambino, M. C. Lombardo, M. Sammartino. 2012-11-19. Pattern formation driven by cross--diffusion in a 2D domain. https://doi.org/10.1016/j.nonrwa.2012.11.009

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