Dresden 2011 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 17: Nonlinear Dynamics I

DY 17.8: Talk

Wednesday, March 16, 2011, 12:30–12:45, ZEU 255

Extractions of non-elliptic limit cycles from strong non-linear oscillations via the modified continuous wavelet transform — •Eugene Postnikov¹ and Elena Lebedeva² — ¹Kursk State University, Kursk, Russia — ²St. Petersburg State Polytechnical University, St. Petersburg, Russia

Recently we have proposed the modification of the complex wavelet transform with the Morlet wavelet adapted for an analysis of strong non-linear oscillations [Phys. Rev. E 82, 057201 (2010)]. It has been shown that the rotation of transform modulus in a scale space allows to merge principal harmonics of non-sinusoidal oscillations into one line corresponding to the scale value coinciding with a main period.

The main goal of this presentation is to analyze the opportunity providing by this method to extract strongly non-elliptic instable limit cycles from chaotic signals. The following items are considered: restrictions, based on time-scale uncertainty, for the maximal number of loops extracted from a phase curve; correspondence between a global cascade of period-doubling bifurcations determined via the Fourier transform and a local loop decomposition based on the wavelet transform; the wavelet decomposition and bounding tori in a phase space.

This work was supported by the grant of the President of the Russian Federation for a support of young researchers Grant No. MK-7413.2010.1