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

Controlling chaos in the system of coupled Chua's oscillators
V.V. Astakhov, A.V. Shabunin, A.N. Silchenko, G.I. Strelkova, V.S. Anishchenko
Department of Physics, Saratov State University,
Saratov, Russia

This work is devoted to the study of natural dynamics and the problems of controlling chaos in the system of coupled identical Chua's oscillators.

For the case of two interacting oscillators, the possible sets of oscillatory regimes and bifurcational transitions for different types of coupling (via capacity and via resistor) were investigated. It has been shown that in the system having several types of symmetry, a chaotic phase trajectory can be stabilized in different symmetrical phase subspaces of the full phase space of the system by menas of small controlling perturbations. It causes the following effects:

1. the controlled transitions from the regimes of developed chaos to the regimes of periodic symmetrical oscillations (for the coupling via capacity);
2. synchronization of in-phase and out-phase chaotic oscillations (for the coupling via capacity and via resistor).

Using the criteria of stability we determined the conditions of stabilization for symmetrical regimes. Detailed numerical and full-scale experiments for controlling chaotic oscillations were carried out when the excitation parameter and coupling coefficient were varied.

Futher spatio-temporal dynamics of the chain of resistively coupled Chua's oscillators were investigated. It has been found that the behavior of this system has the features in comparison with that of the chain of coupled maps. The evolution of various spatio-temporal patterns with temporal period one to the regime of developed chaos is explored. The possibilities of controlling chaos by means of small spatio-temporal perturbations of the systems are studied.