2017
Том 69
№ 5

All Issues

Dynamical Bifurcation of Multifrequency Oscillations in a Fast-Slow System

Parasyuk I. O., Repeta B. V., Samoilenko A. M.


Abstract

We study a dynamical analog of bifurcations of invariant tori for a system of interconnected fast phase variables and slowly varying parameters. It is shown that, in this system, due to the slow evolution of the parameters, we observe the appearance of transient processes (from the damping process to multifrequency oscillations) asymptotically close to motions on the invariant torus.

English version (Springer): Ukrainian Mathematical Journal 67 (2015), no. 7, pp 1008-1037.

Citation Example: Parasyuk I. O., Repeta B. V., Samoilenko A. M. Dynamical Bifurcation of Multifrequency Oscillations in a Fast-Slow System // Ukr. Mat. Zh. - 2015. - 67, № 7. - pp. 890-915.