Year: 2025
Type: preprint
Abstract: The FitzHugh-Nagumo model, originally introduced to study neural dynamics, has since found applications across diverse fields, including cardiology and biology. However, the formation and bifurcation structure of spatially localized states in this model remain underexplored. In this work, we present a detailed bifurcation analysis of such localized structures in one spatial dimension in the FitzHugh-Nagumo model. We demonstrate that these localized states undergo a smooth transition between standard and collapsed homoclinic snaking as the system shifts from pattern-uniform to uniform-uniform bistability. Additionally, we explore the oscillatory dynamics exhibited by these states when varying the time-scale separation and diffusion coefficient. Our study leverages a combination of analytical and numerical techniques to uncover the stability and dynamic regimes of spatially localized structures, offering new insights into the mechanisms governing spatial localization in this widely used model system.
Source: arXiv (Cornell University)
Institutions: University of Almería, KU Leuven
Language: English
Subfield: Computer Networks and Communications
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Funders: KU Leuven, Vlaamse regering
Awards: G1338284348, G628814547
OpenAlex ID: W4406604290