The Quasi-Normal Form of a System of Three Unidirectionally Coupled Singularly Perturbed Equations with Two Delays

• Main Authors: A. S. Bobok, S. D. Glyzin, A. Yu. Kolesov
• Format: Article
• Language: English
• Published: Yaroslavl State University 2013-01-01
• Series: Modelirovanie i Analiz Informacionnyh Sistem
• Subjects: дифференциально-разностное уравнение; бифуркация; квазинормальная форма; буферность
• Online Access: http://mais-journal.ru/jour/article/view/180

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.