Diffusive stability of convective Turing patterns

2021/01/20 by Aric Wheeler, Wheeler, Aric, Kevin Zumbrun +1
Computer Science · Engineering · Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Biology Tumor Growth #Nonlinear Dynamics and Pattern Formation #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2101.08360

openalex publication_date 2021/01/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Following the approach of [E1, M1, M2, S1, S2, SZJV] for reaction diffusion systems, we justify rigorously the Eckhaus stability criterion for stability of convective Turing patterns, as derived formally by complex Ginzburg-Landau approximation [SS, NW, WZ]. Notably, our analysis includes also higher-order, nonlocal, and even certain semilinear hyperbolic systems.

Citations

• The chemical basis of morphogenesis
• Diffusive stability of spatially periodic patterns with a conservation\n law

Related

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• Turing Instabilities and Patterns Near a Hopf Bifurcation
• Diffusive stability of spatially periodic patterns with a conservation\n law
• Pattern formation (II): The Turing Instability
• Nonlinear convective stability of a critical pulled front undergoing a Turing bifurcation at its back: a case study