Geodesic
Investigation of oscillatory solutions of differential-difference equations of~second order in a critical case
Modelirovanie i analiz informacionnyh sistem, Tome 22 (2015) no. 3, pp. 439-447

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We consider a differential-difference equation of second order of delay type, containing the delay of the function and its derivatives. Such equations occur in the modeling of electronic devices. The nature of the loss of the zero solution stability is studied. The possibility of stability loss related to the passing of two pairs of purely imaginary roots, that are in resonance 1:3, through an imaginary axis is shown. In this case bifurcating oscillatory solutions are studied. It is noted the existence of a chaotic attractor for which Lyapunov exponents and Lyapunov dimension are calculated. As an investigation techniques we use the theory of integral manifolds and normal forms method for nonlinear differential equations.
Keywords: $D$-splitting, method of integral manifolds, bifurcation theory
Mots-clés : chaotic oscillations. 
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     title = {Investigation of oscillatory solutions of differential-difference equations of~second order in a critical case},
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     pages = {439--447},
     publisher = {mathdoc},
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     url = {http://geodesic.mathdoc.fr/item/MAIS_2015_22_3_a7/}
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E. P. Kubyshkin; A. R. Moryakova. Investigation of oscillatory solutions of differential-difference equations of~second order in a critical case. Modelirovanie i analiz informacionnyh sistem, Tome 22 (2015) no. 3, pp. 439-447. http://geodesic.mathdoc.fr/item/MAIS_2015_22_3_a7/