ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

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Baranov S. 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: 10.18500/0869-6632-2010-18-1-12-23

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Chaos in the phase dynamics of q­switched van der pol oscillator with additional delayed feedback loop

Baranov Stanislav Vladimirovich, Saratov State University
Kuznetsov Sergey Petrovich, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences
Ponomarenko Vladimir Ivanovich, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences

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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