Based on scalefree coupling topology map lattices, the synchronization dynamics and times of the coupled bothdiscontinuousandnoninvertiblemap lattices and the coupled logisticmap lattices are investigated. The synchronization order parameters, the largest Lyapunov exponents, and the mean synchronization times are calculated under different coupling strengths. The results show that, due to the interplay between the discontinuity and the noninvertibility, the coupled discontinuous map lattices system exhibits complex prelude dynamics for synchronization, and the mean synchronization time varies with the coupling strength nonmonotonously, showing a unimodal curve. These results reveal very different new characteristics against those observed in the coupled logisticmap lattices system.

coupled map lattices; scalefree networks; synchronization; discontinuous map