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Transport Phenomena in Excitable Systems: Existence of Bounded Solutions and Absorbing Sets

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  • Monica De Angelis

    (Department of Mathematics and Applications “R. Caccioppoli”, University of Naples “Federico II”, Via Cinthia 26, 80126 Naples, Italy)

Abstract

In this paper, the transport phenomena of synaptic electric impulses are considered. The FitzHugh–Nagumo and FitzHugh–Rinzel models appear mathematically appropriate for evaluating these scientific issues. Moreover, applications of such models arise in several biophysical phenomena in different fields such as, for instance, biology, medicine and electronics, where, by means of nanoscale memristor networks, scientists seek to reproduce the behavior of biological synapses. The present article deals with the properties of the solutions of the FitzHugh–Rinzel system in an attempt to achieve, by means of a suitable “energy function”, conditions ensuring the boundedness and existence of absorbing sets in the phase space. The results obtained depend on several parameters characterizing the system, and, as an example, a concrete case is considered.

Suggested Citation

  • Monica De Angelis, 2022. "Transport Phenomena in Excitable Systems: Existence of Bounded Solutions and Absorbing Sets," Mathematics, MDPI, vol. 10(12), pages 1-11, June.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:12:p:2041-:d:837263
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    References listed on IDEAS

    as
    1. Capone, F. & Carfora, M.F. & De Luca, R. & Torcicollo, I., 2019. "Turing patterns in a reaction–diffusion system modeling hunting cooperation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 165(C), pages 172-180.
    2. Lin, Y. & Liu, W.B. & Bao, H. & Shen, Q., 2020. "Bifurcation mechanism of periodic bursting in a simple three-element-based memristive circuit with fast-slow effect," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
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