Noise-induced Synchronization of Uncoupled Nonlinear Systems

Abstract

We derive a recursion formulae of transition probability of the noise-induced synchronization arising in a pair of identical uncoupled logistic maps linked by common noisy excitation only. The formulae has a delta-type stationary solution which represents the perfect synchronization with probability 1. The stationary solution maintains under chaotic bifurcation while the escape times to reach the perfect synchronization are increased in the chaotic region. A physical implementation of the synchronization is also demonstrated.