Anishchenko V.S., Astakhov V.V., Strelkova G.I., Shabunin A.V.

Fourier analysis of symmetrically coupled Chua's oscillators
V.S. Anishchenko, V.V. Astakhov, G.I. Strelkova, A.V. Shabunin
Department of Physics, Saratov State University, Russia

The work is devoted to Fourier analysis of the Chua's circuits coupled via resistor or capacity. The investigated system is two symmetrically coupled oscillators with period-doubling [1]. It demonstrates complex evolution from periodic regimes to chaotic attractors as well as multistability phenomenon of the limit sets simultaniously coexisting in phase space of the system [2].

One of the our work aims is to explain similarity of behaviours of different symmetrically coupled oscillators with period-doubling. We compared the dynamics of the system with dynamics of coupled RL-diod circuits forced in-phase and coupled logistic maps [3-4]. These systems are known to be characterised by time-delay between motions of the oscillators which is equal to several periods of original cycle . Besides, there are similar bifurcational transitions between different regimes in these systems.

To investigate interaction and synchronization of oscillators we used the method of phase differencies diagrams [5]. In the work we demonstrate the power spectra and the diagrams of phase differencies for regular and chaotic oscillations of the systems and investigate the laws of their variations with the system evolution. It was found that phase relations which characterize synchronization of the oscillators are kept constant along the whole evolution from cycles to chaos. This property gave us possibility to describe bifurcations of regimes in the systems from the point of view of the Fourier spectrum. Also we found that different chaotic attractors of the circuits can be transformed to each other by using of determine time-delay between motions of the oscillators.

We suppose that these investigations make once more step for uderstanding of the problems of mutual synchronization of oscillators with complex dynamics.

1. L.O. Chua, M. Komyro, T. Matsumoto, IEEE Trans. Circuits Syst., CAS-33 (1986) 1073.
2. V.S. Anishchenko, T.E. Vadivasova, V.V. Astakhov, O.V.  Sosnovtseva, Int.J. Bifurcation and Chaos, 5 (1995).
3. V.V. Astakhov, B.P. Bezruchko, Yu.V. Gulyaev, E.P. Seleznev, Pisma v ZhTF, 15(3) (1989) 60.
4. V.V. Astakhov, B.P. Bezruchko, E.N. Erastova, E.P. Seleznev, ZhTF, 60(10) (1990) 19.
5. V.S. Anishchenko, T.E. Vadivasova, D.E. Postnov, M.A. Safonova , Int.J. Bifurcation and Chaos, 2(3) (1992) 633.