Numerical studies indicate that the FitzHugh–Nagumo system exhibits stable traveling pulses with oscillatory tails. In this paper, the existence of such pulses is proved analytically in the singular perturbation limit near parameter values where the FitzHugh–Nagumo system exhibits folds. In addition, the stability of these pulses is investigated numerically, and a mechanism is proposed that exp...

In this paper, the transport phenomena of synaptic electric impulses are considered. The FitzHugh--Nagumo and FitzHugh--Rinzel models appear mathematically appropriate for evaluating these scientific issues. Moreover, applications such arise in several biophysical different fields as, instance, biology, medicine electronics, where, by means nanoscale memristor networks, scientists seek to repro...

Stochastic differential equation (SDE) models of nerve cells for the most part neglect the spatial dimension. Including the latter leads to stochastic partial differential equations (SPDEs) which allow for the inclusion of important variations in the densities of ion channels. In the first part of this work, we briefly consider representations of neuronal anatomy in the context of linear SPDE m...

We introduce a technique based on algebraic topology for quantifying spatio-temporally chaotic dynamics. The technique is illustrated using the Gray-Scott and the FitzHugh-Nagumo models.

We study the role of strong particle/particle interactions and stochastic fluctuations emanating from the micro-/sub-grid scale, in the context of a simple prototype hybrid system consisting of a scalar linear ordinary differential equation (ODE), coupled to a microscopic spin flip Ising lattice system. Due to the presence of strong interactions in the lattice model, the mean-field approximatio...

The electrophysiology of cardiac myocytes is tightly coupled to mechanics. One aspect of this is apparent in the effects of mechanical strain on cardiac action potential dynamics. These can be considered through adjustments to classic electrophysiological models. The standard FitzHugh Nagumo model is a reduced two-variable model from Hodgkin-Huxley that can reproduce basic mechanisms of action ...

Nonlinear dynamics is a rapidly developing subject across all disciplines involving spatial or temporal evolution. The reconstruction of equations motion for nonlinear system from observed time series has been hot topic long time. Nevertheless, in practice only partial information available many systems which are very likely contaminated with noise. Here, based on the invariance evolution equat...