The wavefront profile and the propagation velocity of waves in an experimentally observed Belousov–Zhabotinskii reaction are analyzed and a revised FitzHumgh–Nagumo (FHN) model of these systems is identified. The ratio between the excitation period and the recovery period, for a solitary wave is studied, and included within the model. Averaged traveling velocities at different spatial positions...

A controller-propagator system with a FitzHugh–Nagumo equation can be reduced to a free boundary problem when a layer parameter ” is equal to zero. We shall show the existence of solutions and the occurence of a Hopf bifurcation for this free boundary problem as the controlling parameter varies. c © 1999 Elsevier Science B.V. All rights reserved. AMS classi cation: primary 35R35; 35B32; seconda...

Chains of N FitzHugh–Nagumo oscillators with a gradient in natural frequencies and strong diffusive coupling are analyzed in this paper. We study the system’s dynamics in the limit of infinitely large coupling and then treat the case when the coupling is large but finite as a perturbation of the former case. In the large coupling limit, the 2N -dimensional phase space has an unexpected structur...

In the first part of this paper [1], a complete description of Q-conditional symmetries for two classes of reaction-diffusion-convection equations with power diffusivities is derived. It was shown that all the known results for reaction-diffusion equations with power diffusivities follow as particular cases from those obtained in [1] but not vise versa. In the second part the symmetries obtaine...

In this paper, a solution of the mathematical model an autowave process in thin nearelectrode layer magnetic fluid is found. A modification FitzHugh–Nagumo system taken as basis made it possible to obtain results similar full-scale experiment. As criterion for adequacy model, we use visual correspondence experiment and presence typical phenomena observed process, such reverbs, pacemakers, bypas...

We develop a data-driven method, based on semi-supervised classification, to predict the asymptotic state of multistable systems when only sparse spatial measurements system are feasible. Our method predicts behavior an observed by quantifying its proximity states in precomputed library data. To quantify this proximity, we introduce sparsity-promoting metric-learning (SPML) optimization, which ...

We consider a general nonlinear diffusion, typified by those deriving from Fitzhugh–Nagumo or Hindmarsh–Rose models of nerve-cell dynamics, perturbed also by 2-parameter white noise. In order to investigate the effects of the nonlinearity, we find for general boundary conditions the mean to order 2 and the four-point covariance to order 3. The derivations involve multiple stochastic integrals i...

A FitzHugh–Nagumo (FHN) model with delayed coupling is considered to investigate the steady state bifurcation due to the coupling strength and delay. The center manifold reduction and normal form method are employed to study the bifurcation from zero singularity. We show that the coupling strength can induce both the pitchfork and transcritical bifurcations and the coupled delay has the most in...

By extending a semi-analytical, dynamical mean-field approximation (DMA) previously proposed by the author [H. Hasegawa, Phys. Rev. E 67, 41903 (2003)], we have developed a generalized theory which takes into account a wide range of couplings in small-world networks consisting of noisy N -unit FitzHugh-Nagumo (FN) neurons: the coordination number on the average Z is allowed to vary from local (...

The FitzHugh–Nagumo model describing propagation of nerve impulses in axons is given by fast-slow reaction-diffusion equations, with dependence on a parameter representing the ratio of time scales. It is well known that for all sufficiently small > 0 the system possesses a periodic traveling wave. With the help of computer-assisted rigorous computations, we prove the existence of this periodic ...