Chaos, noise, and synchronization reconsidered

Abstract

In a recent paper, Maritan and Banavar [Phys. Rev. Lett. 72, 1451 (1994)] reported the synchronization of identical chaotic systems by additive noise. We relate such a synchronization to the maximum Lyapunov exponent of a single system and discuss the underlying mechanisms of the effect. In the case of the Lorenz equations, the nonvanishing mean of the noise mimics a parameter change leading to synchronization. For the logistic map a state dependence of the fluctuations is induced by the boundary conditions.