Title

Stationary Bistable Pulses In Discrete Inhomogeneous Media

Keywords

FitzHugh-Nagumo equation; inhomogeneous diffusion; McKean's caricature; propagation failure; spatially discrete

Abstract

A second-order difference equation with boundary conditions at infinity is solved, and solutions are analysed in terms of problem parameters. The equation describes stationary pulse solutions of differential-difference equations with a nonlinearity known as McKean's caricature of the cubic. The method of solution reduces the nonlinear problem to a linear inhomogeneous problem under certain conditions. The most important feature of the problem is that coefficients of the difference terms are allowed to vary on a finite interval, leading to changes in solution shapes, as well as changes in parameter values that are acceptable for generating solutions to the problem. Formulas for multiple-pulse solutions are derived, while 1-pulse solutions are considered in detail, and the range of parameter values that allow for the existence of stationary pulses is determined. Numerical methods applied to a spatially discrete FitzHugh-Nagumo equation demonstrate the solution stability and the relationship between the existence of stationary pulses and propagation failure of travelling waves. © 2014 © 2014 Taylor & Francis.

Publication Date

1-1-2014

Publication Title

Journal of Difference Equations and Applications

Volume

20

Issue

1

Number of Pages

1-23

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1080/10236198.2013.800868

Socpus ID

84886438482 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84886438482

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