We study a singularly perturbed system of partial differential equations that models a one-dimensional array of coupled Chua’s circuits. The PDE system is a natural generalization to the FitzHugh-Nagumo equation. In part I of the paper, we show that similar to the FitzHugh-Nagumo equation, the system has periodic traveling wave solutions formed alternatively by fast and slow flows. First, asymp...

Differential quadrature method DQM is proposed for the numerical solution of oneand twospace dimensional hyperbolic telegraph equation subject to appropriate initial and boundary conditions. Both polynomial-based differential quadrature PDQ and Fourier-based differential quadrature FDQ are used in space directions while PDQ is made use of in time direction. Numerical solution is obtained by usi...

This paper deals with the problem of state estimation for a hyperbolic equation in the presence of unknown, but bounded disturbances, on the basis of information from sensors with finite-dimensional outputs. The object of investigation is the hyperbolic telegraph equation with energy dissipation. Observability properties similar to those introduced earlier for parabolic systems ([8]) are checke...

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...

We prove the validity of an averaging principle for a class of systems of slow-fast reaction-diffusion 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.

The authors study a type of second order nonlinear telegraph equation. The existence and uniqueness of positive doubly periodic solutions are discussed. The parametric dependence of the solutions is also investigated. Two examples are given as applications of the results.