Transport Phenomena in Excitable Systems: Existence of Bounded Solutions and Absorbing Sets
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 fiel...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-06-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/12/2041 |
| _version_ | 1797484729931399168 |
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| author | Monica De Angelis |
| author_facet | Monica De Angelis |
| author_sort | Monica De Angelis |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-09T23:08:37Z |
| format | Article |
| id | doaj.art-2ee4298f9650409aab33b4883757a6d9 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T23:08:37Z |
| publishDate | 2022-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-2ee4298f9650409aab33b4883757a6d92023-11-23T17:48:45ZengMDPI AGMathematics2227-73902022-06-011012204110.3390/math10122041Transport Phenomena in Excitable Systems: Existence of Bounded Solutions and Absorbing SetsMonica De Angelis0Department of Mathematics and Applications “R. Caccioppoli”, University of Naples “Federico II”, Via Cinthia 26, 80126 Naples, ItalyIn 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.https://www.mdpi.com/2227-7390/10/12/2041transport phenomenaFitzHugh–Rinzel modelabsorbing setsnonlinear dynamicsbiological neuron models |
| spellingShingle | Monica De Angelis Transport Phenomena in Excitable Systems: Existence of Bounded Solutions and Absorbing Sets Mathematics transport phenomena FitzHugh–Rinzel model absorbing sets nonlinear dynamics biological neuron models |
| title | Transport Phenomena in Excitable Systems: Existence of Bounded Solutions and Absorbing Sets |
| title_full | Transport Phenomena in Excitable Systems: Existence of Bounded Solutions and Absorbing Sets |
| title_fullStr | Transport Phenomena in Excitable Systems: Existence of Bounded Solutions and Absorbing Sets |
| title_full_unstemmed | Transport Phenomena in Excitable Systems: Existence of Bounded Solutions and Absorbing Sets |
| title_short | Transport Phenomena in Excitable Systems: Existence of Bounded Solutions and Absorbing Sets |
| title_sort | transport phenomena in excitable systems existence of bounded solutions and absorbing sets |
| topic | transport phenomena FitzHugh–Rinzel model absorbing sets nonlinear dynamics biological neuron models |
| url | https://www.mdpi.com/2227-7390/10/12/2041 |
| work_keys_str_mv | AT monicadeangelis transportphenomenainexcitablesystemsexistenceofboundedsolutionsandabsorbingsets |