Turing instability and traveling fronts for a nonlinear reaction–diffusion system with cross-diffusion

G. Gambino, M.C. Lombardo and M. Sammartino

Mathematics and Computers in Simulation (MATCOM), 2012, vol. 82, issue 6, 1112-1132

Abstract: In this work we investigate the phenomena of pattern formation and wave propagation for a reaction–diffusion system with nonlinear diffusion. We show how cross-diffusion destabilizes uniform equilibrium and is responsible for the initiation of spatial patterns. Near marginal stability, through a weakly nonlinear analysis, we are able to predict the shape and the amplitude of the pattern. For the amplitude, in the supercritical and in the subcritical case, we derive the cubic and the quintic Stuart–Landau equation respectively.

Keywords: Nonlinear diffusion; Pattern formation; Amplitude equation; Quintic Stuart–Landau equation; Ginzburg–Landau equation (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (11)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:82:y:2012:i:6:p:1112-1132

DOI: 10.1016/j.matcom.2011.11.004

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