Experiments on Synchronization and Control of Chaotic Oscillators

摘要

The authors carried out experiments and supporting simulations on the dynamics of nonlinear complex systems with coupling, feedback, external forcing, and noise. The experiments were carried out with arrays of electrodes where: (1) the sites have measurable rates of reaction and can be addressed individually, (2) each site has rich dynamics depending on reactor parameters, and (3) the strength and length scales of coupling among the elements are controllable. The authors have provided a proof of the theory on the emergence of synchronization of coupled smooth oscillators. They demonstrate a phase transition and dependence of order on coupling strength predicted by the theory. Furthermore, they have shown a strong enhancement of fluctuations near the critical point and evidence that the principal predictions also hold for relaxation and weakly chaotic oscillators that often occur in physical systems. For very weak coupling of chaotic systems there are no qualitative effects on local chaotic dynamics. These small effects can nevertheless produce significant changes in the collective, or overall, behavior of the system and the collective behavior can be quite different from the local behavior. The authors also carried out experiments on the application of global coupling, periodic forcing, and feedback to arrays of chaotic electrochemical oscillators. By controlling the external variations or system feedback to influence spatial-temporal patterns and system behavior, desired states (synchronized behavior, cluster formation, etc.) can be obtained. The constructive effects of added noise on synchronization were studied in both small sets and in larger populations of coupled chaotic oscillators. (5 figures).