PHASE SYNCHRONIZATION OF LINEARLY AND NONLINEARLY COUPLED OSCILLATORS WITH INTERNAL RESONANCE

Abstract

Phase synchronization between linearly and nonlinearly coupled systems with internal resonance is investigated in this paper. By introducing the conception of phase for a chaotic motion, it demonstrates that the detuning parameter σ between the two natural frequencies ω1and ω2affects phase dynamics, and with the increase in the linear coupling strength, the effect of phase synchronization between two sub-systems was enhanced, while increased firstly, and then decayed as nonlinear coupling strength increases. Further investigation reveals that the transition of phase states between the two oscillators are related to the critical changes of the Lyapunov exponents, which can also be explained by the diffuse clouds.