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On the foundation of the domestic and international research work, we have used recurrence plot and cross recurrence plot to study the different behavioral form of time series with different characters on its responding recurrence plot and cross recurrence plot. When the time series engender the phenomenon of Lorenz system, stable sink, saddle, bifurcation point and Hopf bifurcation the recurrence plot and cross recurrence plot have also been researched. We have obtained five new kinds of recurrence plots and cross recurrence plots which can provide the evidence to determine the complexity of time series. The result of this research established the base of classification the chaotic time series precisely. This is of important theoretical and practical meaning.