Abstract
The synchronization time in the coupled discontinuous maps is investigated. The results show that the synchronization time of the coupled discontinuous systems exhibits a non-monotonic behaviour as the coupling strength increases. Moreover, a coexistence attractor, which consists of a period state and synchronization one, is found, and it exhibits a riddle basin character. The initial conditions of coupled systems, which is close to the basin boundary of period attractor, can lead to a long quasiperiodic transient, and the trajectory jumps from one region to another one in the phase space. Finally, the non-monotonic behaviour of the synchronization time of the coupled discontinuous systems is also checked in other types of discontinuous maps.
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