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Spikes for Other Two-Component Reaction-Diffusion Systems

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Mathematical Aspects of Pattern Formation in Biological Systems

Part of the book series: Applied Mathematical Sciences ((AMS,volume 189))

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Abstract

We present results on the existence and stability of multiple spikes for reaction-diffusion systems of the activator-substrate type: The Schnakenberg and Gray-Scott models. We will consider the Schnakenberg model in one space dimension and the Gray-Scott model in two space dimensions. We will conclude by considering flow-distributed spikes, namely the influence of convection on the existence and stability of spikes in the case of the Schnakenberg model. In this chapter we focus on the main results and their biological relevance but skip most of the proofs.

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Authors and Affiliations

  1. Department of Mathematics, The Chinese University of Hong Kong, Hong Kong, China

    Juncheng Wei

  2. Department of Mathematical Sciences, Brunel University, Uxbridge, UK

    Matthias Winter

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  1. Juncheng Wei
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  2. Matthias Winter
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Wei, J., Winter, M. (2014). Spikes for Other Two-Component Reaction-Diffusion Systems. In: Mathematical Aspects of Pattern Formation in Biological Systems. Applied Mathematical Sciences, vol 189. Springer, London. https://doi.org/10.1007/978-1-4471-5526-3_10

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