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Heteroclinic connections in a hyperbolic reaction-transport model for excitable media

Author

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  • Grifó, Gabriele
  • Curró, Carmela
  • Valenti, Giovanna

Abstract

This work aims at investigating the emergence of continuous and discontinuous heteroclinic connections arising in an excitable media by means of a hyperbolic extension of the activator–inhibitor Barkley model. In particular, the 1D reaction-transport model is considered to qualitatively depict the behaviour of the fast activator variable and the slow inhibitor one by highlighting the role played by inertia. The occurrence of gradual or abrupt phenomena is analysed by studying the formation of continuous and discontinuous orbits between the steady states. Results emphasize the possibility to observe both colonization or degradation phenomena depending on the combination of the inertial effects and the excited migration speed. Finally, numerical investigation are performed to corroborate the theoretical results and get more details on the system responses to any abrupt or gradual change.

Suggested Citation

  • Grifó, Gabriele & Curró, Carmela & Valenti, Giovanna, 2025. "Heteroclinic connections in a hyperbolic reaction-transport model for excitable media," Chaos, Solitons & Fractals, Elsevier, vol. 200(P3).
    • Handle: RePEc:eee:chsofr:v:200:y:2025:i:p3:s0960077925010434
    DOI: 10.1016/j.chaos.2025.117030
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    References listed on IDEAS

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    1. Consolo, Giancarlo & Grifó, Gabriele & Valenti, Giovanna, 2022. "Dryland vegetation pattern dynamics driven by inertial effects and secondary seed dispersal," Ecological Modelling, Elsevier, vol. 474(C).
    2. Consolo, Giancarlo & Curró, Carmela & Grifó, Gabriele & Valenti, Giovanna, 2024. "Stationary and Oscillatory patterned solutions in three-compartment reaction–diffusion systems: Theory and application to dryland ecology," Chaos, Solitons & Fractals, Elsevier, vol. 186(C).
    3. López Garza, Gabriel & Nicolás Mata, Aurelio & Román Alonso, Graciela & Godínez Fernández, José Rafael & Castro García, Miguel Alfonso, 2022. "Cell-to-cell mathematical modeling of arrhythmia phenomena in the heart," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 193(C), pages 153-172.
    4. Currò, C. & Grifò, G. & Valenti, G., 2023. "Turing patterns in hyperbolic reaction-transport vegetation models with cross-diffusion," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    5. Smidtaite, Rasa & Ragulskis, Minvydas, 2022. "Spiral waves of divergence in the Barkley model of nilpotent matrices," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    6. Cosgun, Tahir & Sari, Murat, 2020. "Traveling wave solutions and stability behaviours under advection dominance for singularly perturbed advection-diffusion-reaction processes," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    7. Sabbagh, Haidar, 2024. "Core expansion and spiral breakup in oscillatory recovering media," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
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    Cited by:

    1. Grifò, Gabriele & Iuorio, Annalisa, 2025. "Travelling pulses in the Barkley model: A geometric singular perturbation approach," Chaos, Solitons & Fractals, Elsevier, vol. 201(P1).

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