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
2013-10-01
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| Series: | Моделирование и анализ информационных систем |
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| Online Access: | https://www.mais-journal.ru/jour/article/view/180 |
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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. |
| format | Article |
| id | doaj-art-253e6284162840e5be823d438836096c |
| institution | Kabale University |
| issn | 1818-1015 2313-5417 |
| language | English |
| publishDate | 2013-10-01 |
| publisher | Yaroslavl State University |
| record_format | Article |
| series | Моделирование и анализ информационных систем |
| spelling | doaj-art-253e6284162840e5be823d438836096c2025-08-20T03:44:18ZengYaroslavl State UniversityМоделирование и анализ информационных систем1818-10152313-54172013-10-0120515816710.18255/1818-1015-2013-5-158-167174The Quasi-Normal Form of a System of Three Unidirectionally Coupled Singularly Perturbed Equations with Two DelaysA. S. Bobok0S. D. Glyzin1A. Yu. Kolesov2P.G. Demidov Yaroslavl State UniversityP.G. Demidov Yaroslavl State UniversityP.G. Demidov Yaroslavl State UniversityWe 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.https://www.mais-journal.ru/jour/article/view/180differential-difference equationbifurcationquasinormal formbuffering |
| 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 differential-difference equation bifurcation quasinormal form buffering |
| 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 | differential-difference equation bifurcation quasinormal form buffering |
| url | https://www.mais-journal.ru/jour/article/view/180 |
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