We prove the validity of an averaging principle for a class of systems of slow-fast reactiondiffusion equations with the reaction terms in both equations having polynomial growth, perturbed by a noise of multiplicative type. The models we have in mind are the stochastic Fitzhugh-Nagumo equation arising in neurophysiology and the Ginzburg-Landau equation arising in statistical mechanics.

Propagation of pulses in myelinated fibers may be described by appropriate solutions of spatially discrete FitzHugh-Nagumo systems. In these systems, propagation failure may occur if either the coupling between nodes is not strong enough or the recovery is too fast. We give an asymptotic construction of pulses for spatially discrete FitzHugh-Nagumo systems which agrees well with numerical simul...

We fabricate a biometric laser fiber synaptic sensor to transmit information from one neuron cell to the other by an optical way. The optical synapse is constructed on the base of an erbium-doped fiber laser, whose pumped diode current is driven by a pre-synaptic FitzHugh-Nagumo electronic neuron, and the laser output controls a post-synaptic FitzHugh-Nagumo electronic neuron. The implemented l...

The FitzHugh-Nagumo equation provides a simple mathematical model of cardiac tissue as an excitable medium hosting spiral wave vortices. Here we present extensive numerical simulations studying long-term dynamics of knotted vortex string solutions for all torus knots up to crossing number 11. We demonstrate that FitzHugh-Nagumo evolution preserves the knot topology for all the examples presente...

In this study, we have done our simulation in two section. In the first step, we simulated the Hodgkin Huxley equations by MATLAB software and obtained the action potential waveform. In the second step, 3D simulation of FitzHugh Nagumo model in order to action potential generation and propagation in squid giant axon have been explored. Simulation of this section has been performed by using the ...

We use geometric singular perturbation techniques combined with an action functional approach to study traveling pulse solutions in a three-component FitzHugh--Nagumo model. First, we derive the profile of 1-pulse undetermined width and propagating speed. Next, compute associated for this from which conditions existence saddle-node bifurcation as zeros its derivatives. obtain same by using diff...

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...

A mathematical model describing the resistance in cell membrane and nerve fiber is proposed, which is naturally different from that for metal conductors. An allometric scaling law between the resistance and the section area is obtained. In the derivation, He Chengtian's interpolation, which has millennia history, is applied. Most famous models, such as the Hodgkin-Huxley model, FitzHugh-Nagumo ...