Characterization of the parameter-mismatching effect on the loss of chaos synchronization

We investigate the effect of the parameter mismatch on the loss of chaos synchronization in coupled one-dimensional maps. Loss of strong synchronization begins with a first transverse bifurcation of a periodic saddle embedded in the synchronous chaotic attractor (SCA), and then the SCA becomes weakly stable. Because of local transverse repulsion of the periodic repellers embedded in the weakly stable SCA, a typical trajectory may have segments of arbitrary length that have positive local transverse Lyapunov exponents. Consequently, the weakly stable SCA becomes sensitive with respect to the variation of the mismatching parameter. To quantitatively characterize such parameter sensitivity, we introduce a quantifier, called the parameter sensitivity exponent (PSE). As the local transverse repulsion of the periodic repellers strengthens, the value of the PSE increases. In terms of these PSEs, we also characterize the parameter-mismatching effect on the intermittent bursting and basin riddling occurring in the regime of weak synchronization.