Travelling pulses in the Barkley model: A geometric singular perturbation approach

Gabriele Grifò and Annalisa Iuorio

Chaos, Solitons & Fractals, 2025, vol. 201, issue P1

Abstract: In this work, we investigate travelling pulse solutions to the Barkley model, a prototypical example of excitable system with activator-inhibitor dynamics. Such patterns are numerically observed for a wide range of parameter values and show how coherent structures can be induced by mechanisms different from diffusion-driven instability. The intrinsic multiscale nature of this system allows us to apply Geometric Singular Perturbation Theory (GSPT) to constructively establish the existence of travelling pulses as homoclinic orbits in the corresponding three-dimensional phase-space. The analytical findings are corroborated by a thorough numerical investigation via direct simulation as well as continuation based on the software AUTO.

Keywords: Travelling pulses; Activator-inhibitor dynamics; Slow-fast dynamics; Geometric singular perturbation theory; Reaction–diffusion models (search for similar items in EconPapers)
Date: 2025
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0960077925013207
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:201:y:2025:i:p1:s0960077925013207

DOI: 10.1016/j.chaos.2025.117307

Access Statistics for this article

Chaos, Solitons & Fractals is currently edited by Stefano Boccaletti and Stelios Bekiros

More articles in Chaos, Solitons & Fractals from Elsevier
Bibliographic data for series maintained by Thayer, Thomas R. ().