An improved pseudospectral approximation of generalized Burger-Huxley and 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...

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

Visual Selection and Attention Shifting Based on FitzHugh-Nagumo Equations

In this paper, we make some analysis on the FitzHugh-Nagumo model and improve it to build a neural network, and the network is used to implement visual selection and attention shifting. Each group of neurons representing one object of a visual input is synchronized; different groups of neurons representing different objects of a visual input are desynchronized. Cooperation and competition mecha...

Mean-field description and propagation of chaos in networks of Hodgkin-Huxley and FitzHugh-Nagumo neurons

We derive the mean-field equations arising as the limit of a network of interacting spiking neurons, as the number of neurons goes to infinity. The neurons belong to a fixed number of populations and are represented either by the Hodgkin-Huxley model or by one of its simplified version, the FitzHugh-Nagumo model. The synapses between neurons are either electrical or chemical. The network is ass...

Variability of Firing of Hodgkin-Huxley and FitzHugh-Nagumo Neurons with Stochastic Synaptic Input

The variability and mean of the firing rate of Hodgkin-Huxley and FitzHugh-Nagumo neurons subjected to random synaptic input are only weakly dependent on the level of inhibitory input, unlike integrate-and-fire neurons. For the latter model, substantial inhibitory input is essential to ensure output variability close to Poissonian firing. It cannot therefore be used routinely in stochastic netw...