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arXiv · 1503.00492

On a kinetic FitzHugh-Nagumo model of neuronal network

Stéphane Mischler·Cristóbal Quiñinao·Jonathan Touboul
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Abstract

We investigate existence and uniqueness of solutions of a McKean-Vlasov evolution PDE representing the macroscopic behaviour of interacting Fitzhugh-Nagumo neurons. This equation is hypoelliptic, nonlocal and has unbounded coefficients. We prove existence of a solution to the evolution equation and non trivial stationary solutions. Moreover, we demonstrate uniqueness of the stationary solution in the weakly nonlinear regime. Eventually, using a semigroup factorisation method, we show exponential nonlinear stability in the small connectivity regime.

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Stéphane Mischler, Cristóbal Quiñinao, Jonathan Touboul. 2015-03-02. On a kinetic FitzHugh-Nagumo model of neuronal network. https://doi.org/10.1007/s00220-015-2556-9

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