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Synchronization of chaos. (English) Zbl 0876.34039

Summary: This paper is devoted to the problem of synchronization of dynamical systems in chaotic oscillations regimes. The authors attempt to use the ideas of synchronization and its mechanisms on a certain class of chaotic oscillations. These are chaotic oscillations for which one can pick out basic frequencies in their power spectra.

The physical and computer experiments were carried out for a system of two coupled auto-oscillators. The experimental installation permitted one to realize both unidirectional coupling (external synchronization) and symmetrical coupling (mutual synchronization). An auto-oscillator with an inertial nonlinearity was chosen as a partial subsystem. It possesses a chaotic attractor of spiral type in its phase space. It is known that such chaotic oscillations have a distinguished peak in the power spectrum at the frequency ${f}_{0}$ (basic frequency). In the experiments, one could make the basic frequencies of partial oscillators equal or different. The bifurcation diagrams on the plane of control parameters “detuning” and “coupling” were constructed and analyzed.

The results of investigations permit one to conclude that classical ideas of synchronization can be applied to chaotic systems of the mentioned type. Two mechanisms of chaos synchronization were established: 1) basic frequency locking and 2) basic frequency suppression. The bifurcational background of these mechanisms was created using numerical analysis on a computer. This allowed one to analyze the evolution of different oscillation characteristics under the influence of synchronization.

##### MSC:
 34C15 Nonlinear oscillations, coupled oscillators (ODE) 37D45 Strange attractors, chaotic dynamics 34D45 Attractors