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 Electronic Journal of Probability > Vol. 13 (2008) > Paper 49 open journal systems 


Stochastic FitzHugh-Nagumo equations on networks with impulsive noise

Stefano Bonaccorsi, Università di Trento
Carlo Marinelli, Universität Bonn
Giacomo Ziglio, Università di Trento


Abstract
We consider a system of nonlinear partial differential equations with stochastic dynamical boundary conditions that arises in models of neurophysiology for the diffusion of electrical potentials through a finite network of neurons. Motivated by the discussion in the biological literature, we impose a general diffusion equation on each edge through a generalized version of the FitzHugh-Nagumo model, while the noise acting on the boundary is described by a generalized stochastic Kirchhoff law on the nodes. In the abstract framework of matrix operators theory, we rewrite this stochastic boundary value problem as a stochastic evolution equation in infinite dimensions with a power-type nonlinearity, driven by an additive Lévy noise. We prove global well-posedness in the mild sense for such stochastic partial differential equation by monotonicity methods.


Full text: PDF

Pages: 1362-1379

Published on: August 25, 2008
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Electronic Journal of Probability. ISSN: 1083-6489