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Spatial localization in the FitzHugh–Nagumo model

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  • Parra-Rivas, Pedro
  • Al Saadi, Fahad
  • Gelens, Lendert

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.

Suggested Citation

  • Parra-Rivas, Pedro & Al Saadi, Fahad & Gelens, Lendert, 2025. "Spatial localization in the FitzHugh–Nagumo model," Chaos, Solitons & Fractals, Elsevier, vol. 201(P2).
    • Handle: RePEc:eee:chsofr:v:201:y:2025:i:p2:s0960077925012603
    DOI: 10.1016/j.chaos.2025.117247
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    References listed on IDEAS

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    1. Michel Fruchart & Ryo Hanai & Peter B. Littlewood & Vincenzo Vitelli, 2021. "Non-reciprocal phase transitions," Nature, Nature, vol. 592(7854), pages 363-369, April.
    2. Akakpo, Edem Kossi & Haelterman, Marc & Leo, Francois & Parra-Rivas, Pedro, 2024. "Implications of tristability on localization phenomena: A necking bifurcation’s tale," Chaos, Solitons & Fractals, Elsevier, vol. 186(C).
    3. Alberto Dinelli & Jérémy O’Byrne & Agnese Curatolo & Yongfeng Zhao & Peter Sollich & Julien Tailleur, 2023. "Non-reciprocity across scales in active mixtures," Nature Communications, Nature, vol. 14(1), pages 1-10, December.
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