| The collective dynamic behavior of a global coupled map lattice composed of a both discontinuous and non-invertible piecewise linear map is studied in this work.There are rich dynamic behavior induced by different mechanisms due to the interaction between the discontinuity and the non-invertibility.The interactions among them may trigger dynamical phenomena with new characteristics.We select the control parameters??0.062 with band-2 chaos for a single map.The relationship between the average order parameter and largest Lyapunov exponent with the coupling strength are calculated to study the synchronization of coupled discontinuous system in this paper.The results indicate that there exists an asynchronous periodic window after the system reaches synchronous state with the increase of the coupling strength.It is found that the system reaches the periodic cluster synchronous state through the spatial amplitude plot,that all nodes of the system are stabled at the period-6 orbits finally.It is found that the stability of the periodic cluster synchronization is related to the size of clusters through the plot of the spatio-temporal evolution,and the stable range of the size of clusters is given.By controlling the size of clusters,the mutual transformation between the periodic cluster synchronization and the chaotic synchronization is achieved,which is of great significance to chaos control.Based on this property,the original high-dimensional system can be simplified to a two-dimensional discontinuous system.By defining the proportion of the synchronization cluster 0<r<1 as another system parameter,the above-mentioned periodic cluster synchronization can be understood and other high period can also be found.By studying the dynamic properties of this two-dimensional coupled discontinuous system,we can better understand the dynamic behavior of high-dimensional coupled discontinuous system. |
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