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arXiv · 2404.13703

Classical solutions of a mean field system for pulse-coupled oscillators: long time asymptotics versus blowup

José Antonio Carrillo·Xu'an Dou·Pierre Roux·Zhennan Zhou
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Abstract

We introduce a novel reformulation of the mean-field system for pulse-coupled oscillators. It is based on writing a closed equation for the inverse distribution function associated to the probability density of oscillators with a given phase in a suitable time scale. This new framework allows to show a hidden contraction/expansion of certain distances leading to a full clarification of the long-time behavior, existence of steady states, rates of convergence, and finite time blow-up of classical solutions for a large class of monotone phase response functions. In the process, we get insights about the origin of obstructions to global-in-time existence and uniform in time estimates on the firing rate of the oscillators.

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José Antonio Carrillo, Xu'an Dou, Pierre Roux, Zhennan Zhou. 2024-04-21. Classical solutions of a mean field system for pulse-coupled oscillators: long time asymptotics versus blowup. https://arxiv.org/abs/2404.13703

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