Synchronization of the stochastic Fitzhugh-Nagumo equations to periodic forcing

Spatially Discrete FitzHugh--Nagumo Equations

We consider pulse and front solutions to a spatially discrete FitzHugh–Nagumo equation that contains terms to represent both depolarization and hyperpolarization of the nerve axon. We demonstrate a technique for deriving candidate solutions for the McKean nonlinearity and present and apply solvability conditions necessary for existence. Our equation contains both spatially continuous and discre...

Analysis of the stochastic FitzHugh-Nagumo system

In this paper we study a system of stochastic differential equations with dissipative nonlinearity which arise in certain neurobiology models. Besides proving existence, uniqueness and continuous dependence on the initial datum, we shall be mainly concerned with the asymptotic behaviour of the solution. We prove the existence of an invariant ergodic measure ν associated with the transition semi...

Qualitative Theory of the FitzHugh-Nagumo Equations

Stochastic Fitzhugh-nagumo Equations on Networks with Impulsive Noise

In this paper we study a system of nonlinear diffusion equations on a finite network in the presence of an impulsive noise acting on the nodes of the system. We allow a rather general nonlinear drift term, including dissipative functions of FitzHugh-Nagumo type (i.e. f(u) = −u(u− 1)(u− a)) arising in various models of neurophysiology (see e.g. the monograph [19] for more details). Electric sign...

Synchronization Properties of Coupled FitzHugh-Nagumo Systems

— We study the synchronized/unsynchronized transition as a function of the noise intensity which appears in a system of globally coupled FitzHugh– Nagumo units under the effect of white noise. By the use of the proper definition of an order parameter, we obtain numerically the phase diagram as a function of the noise intensity and coupling constant.