We investigate a ring of N FitzHugh–Nagumo elements coupled in phase-repulsive fashion and submitted to a (subthreshold) common oscillatory signal and independent Gaussian white noises. This system can be regarded as a reduced version of the one studied in [Phys. Rev. E 64, 041912 (2001)], although externally forced and submitted to noise. The noise-sustained synchronization of the system with ...

The FitzHugh-Rinzel system is able to describe some biophysical phenomena, such as bursting oscillations, and the study of its solutions can help better understand several behaviours complex dynamics biological systems. We express by means an integral equation involving fundamental solution $ H(x,t) related a non linear integro-differential equation. Properties allow us obtain priori estimates ...

We introduce a geometrical extension of the FitzHugh-Nagumo equations describing propagation electrical impulses in nerve axons. In this extension, axon is modeled as warped cylinder, rather than straight line, usually done, while pulses propagate on its surface, case with real prove stability for standard cylinder and existence pulse-like solutions cylinders whose radii are small vary slowly a...

Abstract We consider the existence and first order conditions of optimality for a stochastic optimal control problem inspired by celebrated FitzHugh–Nagumo model, with nonlinear diffusion term, perturbed linear multiplicative Brownian-type noise. The main novelty present paper relies on application rescaling method which allows us to reduce original random one.

We consider the kinetic Fokker–Planck equation with a class of general force. prove existence and uniqueness positive normalized equilibrium (in case force) establish some exponential rate convergence to (and can be explicitly computed). Our results improve about classical force case. result also improves for Fitzhugh–Nagumo from non-quantitative quantitative explicit rate.

The aim of this work is to describe the dynamics a discrete fractional-order reaction–diffusion FitzHugh–Nagumo model. We established acceptable requirements for local asymptotic stability system’s unique equilibrium. Moreover, we employed Lyapunov functional show that constant equilibrium solution globally asymptotically stable. Furthermore, numerical simulations are shown clarify and exemplif...