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SYNCHRONIZATION OF SELF-OSCILLATIONS BY PARAMETRIC EXCITATION



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International Journal of Bifurcation and Chaos Vol 8 No 7 1998 1605 1612 c World Scientific Publishing Company SYNCHRONIZATION OF SELF OSCILLATIONS BY PARAMETRIC EXCITATION V ASTAKHOV A SHABUNIN and V ANISHCHENKO Radiophysics Department Saratov State University Astrahanskaya 83 Saratov Russia Received July 15 1997 Revised November 14 1997 This paper is devoted to the problem of synchronization of symmetrically coupled self oscillators exhibiting chaos by means of chaos control technique We use a nonfeedback method of control in particular high frequency periodic modulation of the coefficient of coupling The model of Chua s circuits coupled via capacity is considered in this work We study the possibility of synchronization in dependence on amplitude and frequency of modulation for various values of the parameters of the self oscillators The dependence of the threshold values of the amplitude of the synchronizing influence on coefficient is presented 1 Introduction Recently much of the interest in nonlinear dynamics has focused on the problem of synchronization of chaotic oscillations Unfortunately there is no common definition of this subject Different authors use different approaches from the classical view on synchronization such as the locking of frequencies Anishchenko et al 1991 1992 and phases Rosenblum et al 1995 to the equality of oscillations in subsystems x1 t x2 t Fujisaka Yamada 1983 Pecora Caroll 1990 Besides investigations of the self synchronization problem there are also tasks of forced synchronization and synchronization by control Lai Grebogi 1993 Chua et al 1993 Astakhov et al 1996a In this paper we investigate the effect of synchronization of symmetrically coupled identical self oscillators applying a high frequency parametric excitation to the coupling element The term synchronization is used here in a narrow sense as motions in the symmetric subspace x1 t x2 t The study of periodic parametric excitation to nonlinear oscillators is a traditional



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