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We consider a system of nonlinear partial differential equations withstochastic dynamical boundary conditions that arises in models ofneurophysiology for the diffusion of electrical potentials through a finitenetwork of neurons. Motivated by the discussion in the biological literature,we impose a general diffusion equation on each edge through a generalizedversion of the FitzHugh-Nagumo model, while the noise acting on the boundary isdescribed by a generalized stochastic Kirchhoff law on the nodes. In theabstract framework of matrix operators theory, we rewrite this stochasticboundary value problem as a stochastic evolution equation in infinitedimensions with a power-type nonlinearity, driven by an additive L\'evy noise.We prove global well-posedness in the mild sense for such stochastic partialdifferential equation by monotonicity methods.

Stochastic FitzHugh-Nagumo equations on networks with impulsive noise