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 Model. Anal. Inform. Sist., 2013, Volume 20, Number 5, Pages 158–167 (Mi mais338)

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

P. G. Demidov Yaroslavl State University, Sovetskaya str., 14, Yaroslavl, 150000, Russia

Abstract: 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.

Keywords: differential-difference equation, bifurcation, quasinormal form, buffering.

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UDC: 517.926

Citation: 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”, Model. Anal. Inform. Sist., 20:5 (2013), 158–167

Citation in format AMSBIB
\Bibitem{BobGlyKol13} \by A.~S.~Bobok, S.~D.~Glyzin, A.~Yu.~Kolesov \paper The Quasi-Normal Form of a System of Three Unidirectionally Coupled Singularly Perturbed Equations with Two Delays \jour Model. Anal. Inform. Sist. \yr 2013 \vol 20 \issue 5 \pages 158--167 \mathnet{http://mi.mathnet.ru/mais338}