CHAOS IN THE PHASE DYNAMICS OF QSWITCHED VAN DER POL OSCILLATOR WITH ADDITIONAL DELAYED FEEDBACK LOOP
Cite this article as:
Baranov . V., Kuznetsov S. P., Ponomarenko V. I. CHAOS IN THE PHASE DYNAMICS OF QSWITCHED VAN DER POL OSCILLATOR WITH ADDITIONAL DELAYED FEEDBACK LOOP. Izvestiya VUZ. Applied Nonlinear Dynamics, 2010, vol. 18, iss. 1, pp. 12-23. DOI: https://doi.org/10.18500/0869-6632-2010-18-1-12-23
We present chaos generator based on a van der Pol oscillator with two additional delayed feedback loops. Oscillator alternately enters active and silence stages due to periodic variation of the parameter responsible for the Andronov–Hopf bifurcation. Excitation of the oscillations on each new activity stage is forced by signal resulting from mixing of the first and the second harmonics of signals from previous activity stages, transported through the feedback loops. The phase difference between each two neighboring succesive activity stages evolves in accordance to the Bernoulli doubling map, with chaotic dynamics. We discuss results of numerical studies: time dependences of variables, attractor portraits, Lyapunov exponents, and power spectrum. The proposed system is implemented as an electronic device, and experimental data are found to be in good correspondence with the computations.
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BibTeX
author = { S. V. Baranov and Sergey P. Kuznetsov and V. I. Ponomarenko},
title = {CHAOS IN THE PHASE DYNAMICS OF QSWITCHED VAN DER POL OSCILLATOR WITH ADDITIONAL DELAYED FEEDBACK LOOP},
year = {2010},
journal = {Izvestiya VUZ. Applied Nonlinear Dynamics},
volume = {18},number = {1},
url = {https://old-andjournal.sgu.ru/en/articles/chaos-in-the-phase-dynamics-of-qswitched-van-der-pol-oscillator-with-additional-delayed},
address = {Саратов},
language = {russian},
doi = {10.18500/0869-6632-2010-18-1-12-23},pages = {12--23},issn = {0869-6632},
keywords = {van der Pol oscillator; Bernoulli doubling map; Smale–Williams solenoid; hyperbolic chaos.},
abstract = {We present chaos generator based on a van der Pol oscillator with two additional delayed feedback loops. Oscillator alternately enters active and silence stages due to periodic variation of the parameter responsible for the Andronov–Hopf bifurcation. Excitation of the oscillations on each new activity stage is forced by signal resulting from mixing of the first and the second harmonics of signals from previous activity stages, transported through the feedback loops. The phase difference between each two neighboring succesive activity stages evolves in accordance to the Bernoulli doubling map, with chaotic dynamics. We discuss results of numerical studies: time dependences of variables, attractor portraits, Lyapunov exponents, and power spectrum. The proposed system is implemented as an electronic device, and experimental data are found to be in good correspondence with the computations. }}