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University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > Existence and Stability of Spike Clusters for Reaction-Diffusion Systems
![]() Existence and Stability of Spike Clusters for Reaction-Diffusion SystemsAdd to your list(s) Download to your calendar using vCal
If you have a question about this talk, please contact webseminars. Coupling Geometric PDEs with Physics for Cell Morphology, Motility and Pattern Formation 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. This talk is included in these lists:
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