EXPERIMENTAL-MEASUREMENT OF THE DEGREE OF CHAOTIC SYNCHRONIZATION USING A DISTRIBUTION EXPONENT

We investigate the use of a distribution exponent for determining the degree of chaotic synchronization of two nearly identical systems. Thi s exponent can be easily measured experimentally; its value correspond s closely to the probability of separation of the two systems, and it is closely connected to the conditional Lyapunov exponent near the thr eshold of synchronization. The determination of the degree of synchron ization by a distribution exponent is illustrated in both experimental and simulated systems of three digital phase locked loops (DPLL's); o ne chaotic ''feeding'' DPLL is an input to two ''receiving'' DPLL's. W e use the relationship between the conditional Lyapunov exponent and t he distribution exponent to evaluate a model of our experimental syste m in which we approximate the feeding chaotic DPLL system with random noise. We determine the degree of synchronization of the two receiving DPLL's by calculating the conditional Lyapunov exponent. The close re lationship between the conditional Lyapunov exponent and distribution exponent at the threshold of synchronization allows us to compare our experimental measurements of synchronization, which use the distributi on exponent, with the conditional Lyapunov exponents calculated from a nalysis.