Geodesic
The Quasi-Normal Form of a System of Three Unidirectionally Coupled Singularly Perturbed Equations with Two Delays
Modelirovanie i analiz informacionnyh sistem, Tome 20 (2013) no. 5, pp. 158-167

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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, buffering.
Mots-clés : bifurcation, quasinormal form 
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     author = {A. S. Bobok and S. D. Glyzin and A. Yu. Kolesov},
     title = {The {Quasi-Normal} {Form} of a {System} of {Three} {Unidirectionally} {Coupled} {Singularly} {Perturbed} {Equations} with {Two} {Delays}},
     journal = {Modelirovanie i analiz informacionnyh sistem},
     pages = {158--167},
     publisher = {mathdoc},
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     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MAIS_2013_20_5_a9/}
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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. Modelirovanie i analiz informacionnyh sistem, Tome 20 (2013) no. 5, pp. 158-167. http://geodesic.mathdoc.fr/item/MAIS_2013_20_5_a9/