Wasserstein contraction for the stochastic Morris-Lecar neuron model
Maxime Herda,
Pierre Monmarché,
Benoît Perthame
Abstract:Neuron models have attracted a lot of attention recently, both in mathematics and neuroscience. We are interested in studying long-time and large-population emerging properties in a simplified toy model. From a mathematical perspective, this amounts to studying the long-time behaviour of a degenerate reflected diffusion process. Using coupling arguments, the flow is proven to be a contraction of the Wasserstein distance for long times, which implies the exponential relaxation toward a (non-explicit) unique glo… Show more
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