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

By Gaetana Gambino, Marco Sammartino, Maria Carmela Lombardo. 2012

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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.

Subfields: Computer Networks and Communications, Genetics, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/559cfc24b52d660315f15afeb6c735e371eec2f9