By introducing the conception of the phase for a chaotic motion,the influence of the linear and nonlinear coupling parameters on the phase synchronization of chaos between two sub-systems was explored.The evolution process from non-synchronized state to imperfect synchronization and further to perfect synchronization between two sub-systems with exact 1:1 internal resonance was discussed.Further investigation reveals that the transition between different phase states is related to the critical change of the Lyapunov exponents.It was pointed out that with the increase of the linear coupling strength,the effect of phase synchronization between two sub-systems was enhanced,while decayed as nonlinear coupling strength increased.
刘勇,王作雷,毕勤胜.具有主共振耦合振子的混沌相位同步[J].动力学与控制学报,2008,6(3):229~234; Liu Yong, Wang Zuolei, Bi Qinsheng. Phase synchronization of coupling oscillators with primary resonance[J]. Journal of Dynamics and Control,2008,6(3):229-234.