Stability and Hopf bifurcation in leech heart interneuron model
This article investigates the activity regimes of a realistic neuron model (as a slow-fast system). The authors study this model using the dynam-ical systems theory, for example, qualitative theory methods of slow-fast systems. The authors obtain the stability conditions of equilibria in leech heart...
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| Format: | Article |
| Language: | English |
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Ferdowsi University of Mashhad
2023-06-01
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| Series: | Iranian Journal of Numerical Analysis and Optimization |
| Subjects: | |
| Online Access: | https://ijnao.um.ac.ir/article_42651_d7803253bb0dfc4b64d36f26539b237f.pdf |
| _version_ | 1797821855691702272 |
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| author | F. Parvizi M. Razvan Y. Alipour Fakhri |
| author_facet | F. Parvizi M. Razvan Y. Alipour Fakhri |
| author_sort | F. Parvizi |
| collection | DOAJ |
| description | This article investigates the activity regimes of a realistic neuron model (as a slow-fast system). The authors study this model using the dynam-ical systems theory, for example, qualitative theory methods of slow-fast systems. The authors obtain the stability conditions of equilibria in leech heart interneurons under defined pharmacological conditions and following Hodgkin–Huxley formalism. Although in neuronal models, the membrane is usually considered capacitance as a fixed parameter, the membrane ca-pacitance parameter is assumed as a control parameter to guarantee the existence of Hopf bifurcation using the Routh–Hurwitz criteria. The au-thors investigate the transition mechanism between the silent phase and tonic spiking mode. Furthermore, some simulations are provided using XPPAUT software for analytical results. |
| first_indexed | 2024-03-13T09:58:57Z |
| format | Article |
| id | doaj.art-ad6072c9bc254c0c9a1220e1ec335e20 |
| institution | Directory Open Access Journal |
| issn | 2423-6977 2423-6969 |
| language | English |
| last_indexed | 2024-03-13T09:58:57Z |
| publishDate | 2023-06-01 |
| publisher | Ferdowsi University of Mashhad |
| record_format | Article |
| series | Iranian Journal of Numerical Analysis and Optimization |
| spelling | doaj.art-ad6072c9bc254c0c9a1220e1ec335e202023-05-23T10:42:00ZengFerdowsi University of MashhadIranian Journal of Numerical Analysis and Optimization2423-69772423-69692023-06-0113217018610.22067/ijnao.2022.75087.110142651Stability and Hopf bifurcation in leech heart interneuron modelF. Parvizi0M. Razvan1Y. Alipour Fakhri2Department of Mathematics, Payame Noor University(PNU), Tehran, Iran.Department of Mathematics, Faculty of Mathematical Sciences, University of Sharif, Tehran, Iran.Department of Mathematics, Payame Noor University(PNU), Tehran, Iran.This article investigates the activity regimes of a realistic neuron model (as a slow-fast system). The authors study this model using the dynam-ical systems theory, for example, qualitative theory methods of slow-fast systems. The authors obtain the stability conditions of equilibria in leech heart interneurons under defined pharmacological conditions and following Hodgkin–Huxley formalism. Although in neuronal models, the membrane is usually considered capacitance as a fixed parameter, the membrane ca-pacitance parameter is assumed as a control parameter to guarantee the existence of Hopf bifurcation using the Routh–Hurwitz criteria. The au-thors investigate the transition mechanism between the silent phase and tonic spiking mode. Furthermore, some simulations are provided using XPPAUT software for analytical results.https://ijnao.um.ac.ir/article_42651_d7803253bb0dfc4b64d36f26539b237f.pdfstabilityhopf bifurcationrouth–hurwitz criteria |
| spellingShingle | F. Parvizi M. Razvan Y. Alipour Fakhri Stability and Hopf bifurcation in leech heart interneuron model Iranian Journal of Numerical Analysis and Optimization stability hopf bifurcation routh–hurwitz criteria |
| title | Stability and Hopf bifurcation in leech heart interneuron model |
| title_full | Stability and Hopf bifurcation in leech heart interneuron model |
| title_fullStr | Stability and Hopf bifurcation in leech heart interneuron model |
| title_full_unstemmed | Stability and Hopf bifurcation in leech heart interneuron model |
| title_short | Stability and Hopf bifurcation in leech heart interneuron model |
| title_sort | stability and hopf bifurcation in leech heart interneuron model |
| topic | stability hopf bifurcation routh–hurwitz criteria |
| url | https://ijnao.um.ac.ir/article_42651_d7803253bb0dfc4b64d36f26539b237f.pdf |
| work_keys_str_mv | AT fparvizi stabilityandhopfbifurcationinleechheartinterneuronmodel AT mrazvan stabilityandhopfbifurcationinleechheartinterneuronmodel AT yalipourfakhri stabilityandhopfbifurcationinleechheartinterneuronmodel |