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

Monica De Angelis
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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

Mathematics, 2022, vol. 10, issue 12, 1-11

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.

Keywords: transport phenomena; FitzHugh–Rinzel model; absorbing sets; nonlinear dynamics; biological neuron models (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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