Pattern formation (II): The Turing Instability

2005/10/19 by Yan Guo, Guo, Yan, Hyung Ju Hwang +1
Computer Science · Engineering · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Biology Tumor Growth #Nonlinear Dynamics and Pattern Formation #Slime Mold and Myxomycetes Research

paper · pdf · doi:10.48550/arxiv.math/0510419

openalex publication_date 2005/10/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the classical Turing instability in a reaction-diffusion system as the secend part of our study on pattern formation. We prove that nonlinear dynamics of a general perturbation of the Turing instability is determined by the finite number of linear growing modes over a time scale of ln(1/δ), where &δ is the strength of the initial perturbation.

Citations

• The chemical basis of morphogenesis
• Instability of periodic BGK equilibria

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