Characterization of the noise effect on weak synchronization

Abstract

We investigate the noise effect on weak synchronization in two coupled identical one-dimensional (1D) maps. Due to the existence of positive local transverse Lyapunov exponents, the weakly stable synchronous chaotic attractor (SCA) becomes sensitive with respect to the variation of noise intensity. To quantitatively characterize such noise sensitivity, we introduce a quantifier, called the noise sensitivity exponent (NSE). For the case of bounded noise, the values of the NSE are found to be the same as those of the exponent characterizing a parameter sensitivity of the weakly stable SCA in presence of a parameter mismatch between the two 1D maps. Furthermore, it is found that the scaling exponent for the average time spent near the diagonal for both the bubbling and riddling cases occurring in the regime of weak synchronization is given by the reciprocal of the NSE, as in the parameter-mismatching case. Consequently, both the noise and parameter mismatch have the same effect on the scaling behavior of the average characteristic time.