Study of neurons plays a key role in the fields of basic and medical research aiming at the development of electrically active implants. The Fitzhugh-Nagumo equations are used to model and simulate the spike generation and propagation in a squid giant axon using Comsol Multiphysics® 3.5a Software. It is shown that the Fitzhugh-Nagumo equations allow for a geometrical explanation of important bi...

We investigate the dynamics of weakly-modulated nonlinear wave trains. For reaction-diffusion systems and for the complex Ginzburg–Landau equation, we establish rigorously that slowly varying modulations of wave trains are well approximated by solutions to the Burgers equation over the natural time scale. In addition to the validity of the Burgers equation, we show that the viscous shock profil...

In this paper, a FitzHugh-Nagumo model with time delays is investigated. The linear stability of the equilibrium and the existence of Hopf bifurcation with delay τ is investigated. By applying Nyquist criterion, the length of delay is estimated for which stability continues to hold. Numerical simulations for justifying the theoretical results are illustrated. Finally, main conclusions are given...

The paper studies the excitability properties of a generalized FitzHugh-Nagumo model. The model differs from the purely competitive FitzHugh-Nagumo model in that it accounts for the effect of cooperative gating variables such as activation of calcium currents. Excitability is explored by unfolding a pitchfork bifurcation that is shown to organize five different types of excitability. In additio...

This work explores four nonlinear classical models of neural oscillators, the HodgkinHuxley model, the Fitzhugh-Nagumo model, the Morris-Lecar model, and the Hindmarsh-Rose model. Nonlinear contraction theory is used to develop observers and perform synchronization analysis on these systems. Neural oscillation and signaling models are based on the biological function of the neuron, with behavio...

This article presents a mathematical and experimental model of neuronal oscillator with memristor-based nonlinearity. The describes the dynamics an electronic circuit implementing FitzHugh–Nagumo neuron model. A nonlinear component this is Au/Zr/ZrO2(Y)/TiN/Ti memristive device. device fabricated on oxidized silicon substrate using magnetron sputtering. such nonlinearity described by three-dime...

In this article, we perform a numerical stability and convergence analysis of the constrained runs initialization scheme for a lattice Boltzmann model. Gear and Kevrekidis developed this scheme in the context of coarse-grained equation-free computing. Given the macroscopic initial fields, we study the mapping of these variables to the higher-dimensional space of lattice Boltzmann variables. The...