Abstract
Transitions to measure synchronization both in the quasiperiodic and chaotic cases are investigated based on numerical computation of two coupled phi(4) equations. Some relevant quantities such as the bare energies, the interaction energy, and the phase difference of the two oscillators are computed to clarify the characteristics of the transitions and the measure-synchronous states. A bifurcation with discontinuous bare energy and continuous interaction energy, which takes the maximum value at the critical point, is found for the transition from the desynchronous quasiperiodic state to the measure-synchronous quasiperiodic state, and the related power law scalings are deduced. Stick-slip and random-walk-like behavior of the phase difference is found for the chaotic measure-synchronous state, and this explains the monotonous increase of the interaction energy with an increase of coupling.
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