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Kuznetsov S. P., Sokha Y. I. Hyperchaos in model nonautonomous system with a cascade excitation transmission through the spectrum. Izvestiya VUZ. Applied Nonlinear Dynamics, 2010, vol. 18, iss. 3, pp. 24-32. DOI: 10.18500/0869-6632-2010-18-3-24-32

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Hyperchaos in model nonautonomous system with a cascade excitation transmission through the spectrum

Kuznetsov Sergey Petrovich, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences
Sokha Yury Ivanovich, Saratov State University

One of the key turbulence theory idea is a cascade energy transmission through the spectrum from large to small scales. It appears that this idea could be used for complex dynamics realization in a different-nature systems even when equations are knowingly differ from hydrodynamical. The system of four van der Pol oscillators is considered in this paper. Chaos generation is realized by cascade excitation transmission from one oscillator to another with frequency doubling. Due to slow forced modulation of the parameters responsible for the self-excitation two pair of oscillators become active turn by turn. In the beginning of each new active stage the excitation of oscillators from second to fourth are stimulated by oscillators with the half frequencies through quadratic nonlinear element. Excitation from the last oscillator to the first one is transmitted by the signal accepted via quadratic nonlinearity in the presence of auxiliary harmonic signal. In accordance with the results of numeric investigation the two positive Lyapunov exponents hyperchaos mode takes place.

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