Diffusive stability of spatially periodic solutions of the Brusselator model

Abstract

Applying the Lyapunov-Schmidt reduction approach introduced by Mielke and Schneider in their analysis of the fourth-order scalar Swift-Hohenberg equation, we carry out a rigorous small-amplitude stability analysis of Turing patterns for the canonical second-order system of reaction diffusion equations given by the Brusselator model. Our results confirm that stability is accurately predicted in the small-amplitude limit by the formal Ginzburg Landau amplitude equations, rigorously validating the standard weakly unstable approximation and Eckhaus criterion.

References in corpus (4)

• Turing pattern formation in the Brusselator system with nonlinear diffusion
• Nonlocalized modulation of periodic reaction diffusion waves: The Whitham equation
• Nonlocalized modulation of periodic reaction diffusion waves: Nonlinear stability
• Nonlinear stability of spatially-periodic traveling-wave solutions of systems of reaction diffusion equations

Cited by in corpus (3)

• Turing patterns in parabolic systems of conservation laws and numerically observed stability of periodic waves
• Nonlinear stability and asymptotic behavior of periodic wave trains in reaction-diffusion systems against $C_{\mathrm{ub}}$-perturbations
• Diffusive stability of convective Turing patterns