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

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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.
Lingua originaleEnglish
pagine (da-a)1755-1779
Numero di pagine25
RivistaNonlinear Analysis: Real World Applications
Volume14 (3)
Stato di pubblicazionePublished - 2013

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All Science Journal Classification (ASJC) codes

  • Medicine(all)
  • Analysis
  • Engineering(all)
  • Economics, Econometrics and Finance(all)
  • Computational Mathematics
  • Applied Mathematics

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