Boundary value problems for the Fitzhugh-Nagumo equations

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...

Qualitative Theory of the FitzHugh-Nagumo Equations

FitzHugh-Nagumo equations with generalized diffusive coupling.

The aim of this work is to investigate the dynamics of a neural network, in which neurons, individually described by the FitzHugh-Nagumo model, are coupled by a generalized diffusive term. The formulation we are going to exploit is based on the general framework of graph theory. With the aim of defining the connection structure among the excitable elements, the discrete Laplacian matrix plays a...

Boundary value problems for strongly nonlinear equations under a Wintner-Nagumo growth condition

where a is a continuous positive function, φ is a strictly increasing homeomorphism and f is a Carathéodory function. In this framework, results on the solvability of boundary value problems, both in compact intervals and on the whole real line, were established (see [9, 10]). Finally, for results concerning differential inclusions or non-autonomous differential operators, see [11, 12] and [13]...

Rotating wave solutions of the FitzHugh-Nagumo equations.

This paper will treat the bifurcation and numerical simulation of rotating wave (RW) solutions of the FitzHugh-Nagumo (FHN) equations. These equations are often used as a simple mathematical model of excitable media. The dependence of the solutions on a uniformly applied current, and also on the diffusion coefficients or domain size will be studied. Ranges of applied current and/or diffusion co...