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Academic Journal
The Quasi-Normal Form of a System of Three Unidirectionally Coupled Singularly Perturbed Equations with Two Delays
A. S. Bobok, S. D. Glyzin, A. Yu. Kolesov
Моделирование и анализ информационных систем, Vol 20, Iss 5, Pp 158-167 (2013)
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| Title | The Quasi-Normal Form of a System of Three Unidirectionally Coupled Singularly Perturbed Equations with Two Delays |
|---|---|
| Authors | A. S. Bobok, S. D. Glyzin, A. Yu. Kolesov |
| Publication Year |
2013
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| Source |
Моделирование и анализ информационных систем, Vol 20, Iss 5, Pp 158-167 (2013)
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| 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.
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| Document Type |
article
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| Language |
English
Russian |
| Publisher Information |
Yaroslavl State University, 2013.
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| Subject Terms | |
