Formation and Persistence of Spatiotemporal Turing Patterns

Hans G. Kaper; Shouhong Wang; Masoud Yari

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arXiv · 0706.2309

Formation and Persistence of Spatiotemporal Turing Patterns

Hans G. Kaper·Shouhong Wang·Masoud Yari

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Abstract

This article is concerned with the stability and long-time dynamics of structures arising from a structureless state. The paradigm is suggested by developmental biology, where morphogenesis is thought to result from a competition between chemical reactions and spatial diffusion. A system of two reaction-diffusion equations for the concentrations of two morphogens is reduced to a finite system of ordinary differential equations. The stability of bifurcated solutions of this system is analyzed, and the long-time asymptotic behavior of the bifurcated solutions is established rigorously. The Schnakenberg and Gierer-Meinhardt equations are discussed as examples.

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Hans G. Kaper, Shouhong Wang, Masoud Yari. 2007-06-15. Formation and Persistence of Spatiotemporal Turing Patterns. https://arxiv.org/abs/0706.2309

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