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

2013

Моделирование и анализ информационных систем, Vol 20, Iss 5, Pp 158-167 (2013)

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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Yaroslavl State University, 2013.

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