Journal
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
Volume 14, Issue 3, Pages 1755-1779Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.nonrwa.2012.11.009
Keywords
Nonlinear diffusion; Turing instability; Amplitude equations; Subcritical bifurcation
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Funding
- INDAM
- Department of Mathematics, University of Palermo
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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. (C) 2012 Elsevier Ltd. All rights reserved.
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