The Quasi-Normal Form of a System of Three Unidirectionally Coupled Singularly Perturbed Equations with Two Delays
We consider a system of three unidirectionally coupled singularly perturbed scalar nonlinear differential-difference equations with two delays that simulate the electrical activity of the ring neural associations. It is assumed that for each equation at critical values of the parameters there is a c...
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| Format: | Article |
| Language: | English |
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Yaroslavl State University
2013-01-01
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| Series: | Моделирование и анализ информационных систем |
| Subjects: | |
| Online Access: | http://mais-journal.ru/jour/article/view/180 |
| _version_ | 1797965972036911104 |
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| author | A. S. Bobok S. D. Glyzin A. Yu. Kolesov |
| author_facet | A. S. Bobok S. D. Glyzin A. Yu. Kolesov |
| author_sort | A. S. Bobok |
| collection | DOAJ |
| description | We consider a system of three unidirectionally coupled singularly perturbed scalar nonlinear differential-difference equations with two delays that simulate the electrical activity of the ring neural associations. It is assumed that for each equation at critical values of the parameters there is a case of an infinite dimensional degeneration. Further, we constructed a quasi-normal form of this system, provided that the bifurcation parameters are close to the critical values and the coupling coefficient is suitably small. In analyzing this quasi-normal form, we can state on the base of the accordance theorem, that any preassigned finite number of stable periodic motions can co-exist in the original system under the appropriate choice of the parameters in the phase space. |
| first_indexed | 2024-04-11T02:07:22Z |
| format | Article |
| id | doaj.art-6e4514d85cd7476587035a70ecbf3b2b |
| institution | Directory Open Access Journal |
| issn | 1818-1015 2313-5417 |
| language | English |
| last_indexed | 2024-04-11T02:07:22Z |
| publishDate | 2013-01-01 |
| publisher | Yaroslavl State University |
| record_format | Article |
| series | Моделирование и анализ информационных систем |
| spelling | doaj.art-6e4514d85cd7476587035a70ecbf3b2b2023-01-03T02:49:36ZengYaroslavl State UniversityМоделирование и анализ информационных систем1818-10152313-54172013-01-01205158167174The Quasi-Normal Form of a System of Three Unidirectionally Coupled Singularly Perturbed Equations with Two DelaysA. S. Bobok0S. D. Glyzin1A. Yu. Kolesov2Ярославский государственный университет им. П.Г. ДемидоваЯрославский государственный университет им. П.Г. ДемидоваЯрославский государственный университет им. П.Г. ДемидоваWe consider a system of three unidirectionally coupled singularly perturbed scalar nonlinear differential-difference equations with two delays that simulate the electrical activity of the ring neural associations. It is assumed that for each equation at critical values of the parameters there is a case of an infinite dimensional degeneration. Further, we constructed a quasi-normal form of this system, provided that the bifurcation parameters are close to the critical values and the coupling coefficient is suitably small. In analyzing this quasi-normal form, we can state on the base of the accordance theorem, that any preassigned finite number of stable periodic motions can co-exist in the original system under the appropriate choice of the parameters in the phase space.http://mais-journal.ru/jour/article/view/180дифференциально-разностное уравнениебифуркацияквазинормальная формабуферность |
| spellingShingle | A. S. Bobok S. D. Glyzin A. Yu. Kolesov The Quasi-Normal Form of a System of Three Unidirectionally Coupled Singularly Perturbed Equations with Two Delays Моделирование и анализ информационных систем дифференциально-разностное уравнение бифуркация квазинормальная форма буферность |
| title | The Quasi-Normal Form of a System of Three Unidirectionally Coupled Singularly Perturbed Equations with Two Delays |
| title_full | The Quasi-Normal Form of a System of Three Unidirectionally Coupled Singularly Perturbed Equations with Two Delays |
| title_fullStr | The Quasi-Normal Form of a System of Three Unidirectionally Coupled Singularly Perturbed Equations with Two Delays |
| title_full_unstemmed | The Quasi-Normal Form of a System of Three Unidirectionally Coupled Singularly Perturbed Equations with Two Delays |
| title_short | The Quasi-Normal Form of a System of Three Unidirectionally Coupled Singularly Perturbed Equations with Two Delays |
| title_sort | quasi normal form of a system of three unidirectionally coupled singularly perturbed equations with two delays |
| topic | дифференциально-разностное уравнение бифуркация квазинормальная форма буферность |
| url | http://mais-journal.ru/jour/article/view/180 |
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