Synchronization time in two coupled cluster networks based on discontinuous map

Abstract

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.