Noise-induced synchronization of uncoupled nonlinear systems

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 increase in the chaotic region. The escape times analysis implies existence of lower dimensional dynamics around the perfect synchronization. We also provide a physical implementation of the synchronization.