Phase synchronization of two coupled Rossler oscillators with internal resonance

Phase synchronization between linearly and nonlinearlycoupled systems with internal resonance was investigated in this paper. Theconception of phase for a chaotic motion was introduced to demonstrate theeffect of the detuning parameter \sigma between the two naturalfrequencies \omega _1 and \omega _2 on the phase dynamics. The resultsshowed that phase synchronization between two subsystems was enhanced withthe increase of the linear coupling strength and decayed with the increaseof nonlinear coupling strength. Further investigation reveals that thetransition of phase states between the two oscillators are related to thecritical changes of the Lyapunov exponents.