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Existence and Stability of Spike Clusters for Reaction-Diffusion Systems

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We study the existence and stability of spike clusters for biological reaction-diffusion systems with two small diffusion constants. In particular we consider a consumer chain model and the Gierer-Meinhardt system with a precursor gradient. In a spike cluster the spikes converge to the same limiting point. We will present results on the asymptotic behaviour of the spikes including their shapes, positions, and amplitudes. We will also compute the asymptotic behaviour of the eigenvalues. Such systems and their solutions play an important role in biological modelling to account for the bridging of lengthscales, e.g. between genetic, nuclear, intra cellular, cellular and tissue levels, or for the hierarchy of biological processes, e.g. first a large scale structure appears and then it induces patterns on a smaller scale. This is joint work with Juncheng Wei.

This talk is part of the Isaac Newton Institute Seminar Series series.

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