Non-Classical Relaxation Oscillations in Neurodynamics
A modification of the well-known FitzHugh–Nagumo model from neuroscience is proposed. This model is a singularly perturbed system of ordinary differential equations with a fast variable and a slow one. The existence and stability of a nonclassical relaxation cycle in this system are studied. The slo...
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| Format: | Article |
| Language: | English |
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Yaroslavl State University
2014-04-01
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| Series: | Моделирование и анализ информационных систем |
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| Online Access: | https://www.mais-journal.ru/jour/article/view/121 |
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| author | S. D. Glyzin A. Yu. Kolesov N. Kh. Rozov |
| author_facet | S. D. Glyzin A. Yu. Kolesov N. Kh. Rozov |
| author_sort | S. D. Glyzin |
| collection | DOAJ |
| description | A modification of the well-known FitzHugh–Nagumo model from neuroscience is proposed. This model is a singularly perturbed system of ordinary differential equations with a fast variable and a slow one. The existence and stability of a nonclassical relaxation cycle in this system are studied. The slow component of the cycle is asymptotically close to a discontinuous function, while the fast component is a δ-like function. A onedimensional circle of unidirectionally coupled neurons is considered. It is shown the existence of an arbitrarily large number of traveling waves for this chain. In order to illustrate the increasing of the number of stable traveling waves numerical methods were involved. |
| format | Article |
| id | doaj-art-b062643efc7c423aabb62e08efbb65af |
| institution | DOAJ |
| issn | 1818-1015 2313-5417 |
| language | English |
| publishDate | 2014-04-01 |
| publisher | Yaroslavl State University |
| record_format | Article |
| series | Моделирование и анализ информационных систем |
| spelling | doaj-art-b062643efc7c423aabb62e08efbb65af2025-08-20T03:22:04ZengYaroslavl State UniversityМоделирование и анализ информационных систем1818-10152313-54172014-04-01212718910.18255/1818-1015-2014-2-71-89115Non-Classical Relaxation Oscillations in NeurodynamicsS. D. Glyzin0A. Yu. Kolesov1N. Kh. Rozov2P.G. Demidov Yaroslavl State UniversityP.G. Demidov Yaroslavl State UniversityM.V. Lomonosov Moscow State UniversityA modification of the well-known FitzHugh–Nagumo model from neuroscience is proposed. This model is a singularly perturbed system of ordinary differential equations with a fast variable and a slow one. The existence and stability of a nonclassical relaxation cycle in this system are studied. The slow component of the cycle is asymptotically close to a discontinuous function, while the fast component is a δ-like function. A onedimensional circle of unidirectionally coupled neurons is considered. It is shown the existence of an arbitrarily large number of traveling waves for this chain. In order to illustrate the increasing of the number of stable traveling waves numerical methods were involved.https://www.mais-journal.ru/jour/article/view/121impuls neuronfitzhugh–nagumo modelrelaxation cycleasymptoticsstabilitybuffering |
| spellingShingle | S. D. Glyzin A. Yu. Kolesov N. Kh. Rozov Non-Classical Relaxation Oscillations in Neurodynamics Моделирование и анализ информационных систем impuls neuron fitzhugh–nagumo model relaxation cycle asymptotics stability buffering |
| title | Non-Classical Relaxation Oscillations in Neurodynamics |
| title_full | Non-Classical Relaxation Oscillations in Neurodynamics |
| title_fullStr | Non-Classical Relaxation Oscillations in Neurodynamics |
| title_full_unstemmed | Non-Classical Relaxation Oscillations in Neurodynamics |
| title_short | Non-Classical Relaxation Oscillations in Neurodynamics |
| title_sort | non classical relaxation oscillations in neurodynamics |
| topic | impuls neuron fitzhugh–nagumo model relaxation cycle asymptotics stability buffering |
| url | https://www.mais-journal.ru/jour/article/view/121 |
| work_keys_str_mv | AT sdglyzin nonclassicalrelaxationoscillationsinneurodynamics AT ayukolesov nonclassicalrelaxationoscillationsinneurodynamics AT nkhrozov nonclassicalrelaxationoscillationsinneurodynamics |