On a Kinetic Fitzhugh–Nagumo Model of Neuronal Network
نویسندگان
چکیده
We investigate existence and uniqueness of solutions of a McKeanVlasov 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. Acknowledgments: This work has been partially supported by ANR project Kibord ANR-13-BS01-0004.
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