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

  • Autori: Gambino, G.; Lombardo, M.; Sammartino, M.
  • Anno di pubblicazione: 2013
  • Tipologia: Articolo in rivista (Articolo in rivista)
  • Parole Chiave: Nonlinear diffusion; Turing instability; Amplitude equations; Subcritical bifurcation
  • OA Link:


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.