We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
On a Kinetic Fitzhugh-Nagumo Model of Neuronal Network.
- Authors
Mischler, S.; Quiñinao, C.; Touboul, J.
- 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.
- Subjects
MATHEMATICAL models; UNIQUENESS (Mathematics); NONLINEAR analysis; EVOLUTION equations; HYPOELLIPTIC differential equations
- Publication
Communications in Mathematical Physics, 2016, Vol 342, Issue 3, p1001
- ISSN
0010-3616
- Publication type
Article
- DOI
10.1007/s00220-015-2556-9