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The aim of this poster is to contribute to the understanding of stability of steady states of systems of ordinary differential equations coupled to reaction-diffusion equations. Such systems arise naturally from the modeling of biological phenomena such as cell-receptor-ligand binding, so called receptor-based models. We present conditions for stability of irregular, discontinuous steady states of a system of one ordinary differential equation coupled to one reaction-diffusion equation. Moreover, we present a model exhibiting Diffusion-Driven Instability and stable discontinuous irregular steady states, i.e. de-novo formation of discontinuous, non-periodic stable steady states. The presentation is based on a joint work with A. Marciniak-Czochra (University of Heidelberg) and I. Takagi (Tohoku University). |
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