Multiple front standing waves in 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...

Standing waves in the FitzHugh-Nagumo model of cardiac electrical activity.

When excitable media are submitted to appropriate time dependent boundary conditions, a standing wavelike pattern can be observed in the system, as shown in recent experiments. In the present analysis, the physical mechanism explaining the occurrence of such space-time patterns is shown to be a competition between Ohmic diffusion and an action potential propagation across the system, coupled wi...

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...

Response functions of spiral waves in the FitzHugh-Nagumo system

Spiral waves are rotating solutions of nonlinear reaction-diffusion systems in two spatial dimensions. Due to the symmetries of the plane, a spiral wave can be shifted and rotated arbitrary, still remaining a solution to reaction-diffusion system. Introducing a symmetry-breaking perturbation of the reaction-diffusion equation, the spiral wave begins to drift, i.e. change its rotation phase and ...