Travelling Fronts, Pulses, and Pulse Trains in a 1D discrete Reaction-Diffusion System
| dc.creator | Majudar, Priyadarshi | |
| dc.creator | Lahiri, Avijit | |
| dc.date | 2004-12-10 | |
| dc.date.accessioned | 2026-07-07T05:36:08Z | |
| dc.date.available | 2026-07-07T05:36:08Z | |
| dc.description | We follow up an earlier work (briefly reviewed below) to investigate the temporal stability of an exact travelling front solution, constructed in the form of an integral expression, for a one-dimensional discrete Nagumo-like model without recovery. Since the model is a piecewise linear one with an on-site reaction function involving a Heaviside step function, a straightforward linearisation around the front solution presents problems, and we follow an alternative approach in estimating a `stability multiplier' by looking at the variational problem as a succession of linear evolution of the perturbations, punctuated with `kicks' of small but finite duration. The perturbations get damped during the linear evolution, while the kicks amplify only the perturbations located at specific sites (the `significant perturbations', see below) with reference to the propagating front. Comparison is made with results of numerical integration of the reaction-diffusion system whereby it appears likely that the travelling front is temporally stable for all parameter values characterising the model for which it exists. We modify the system by introducing a slow variation of a relevant recovery parameter and perform a leading order singular perturbation analysis to construct a pulse solution in the resulting model. In addition, we obtain (in the leading order) a 1-parameter family of periodic pulse trains for the system, modelling re-entrant pulses in a one-dimensional ring of excitable cells. | |
| dc.description | 26 pages, 13 figures | |
| dc.identifier | https://arxiv.org/abs/nlin/0412030 | |
| dc.identifier | http://arxiv.org/abs/nlin/0412030 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/80891 | |
| dc.subject | Pattern Formation and Solitons | |
| dc.title | Travelling Fronts, Pulses, and Pulse Trains in a 1D discrete Reaction-Diffusion System | |
| dc.type | text |