Ordered slow and fast dynamics of unsynchronized coupled phase oscillators

Slow and fast dynamics of unsynchronized coupled nonlinear oscillators is hard to extract. In this paper, we use the concept of perpetual points to explain the short duration ordering in the unsynchronized motions of the phase oscillators. We show that the coupled unsynchronized system has ordered slow and fast dynamics when it passes through the perpetual point. Our simulations of single, two, three, and 50 coupled Kuramoto oscillators show the generic nature of perpetual points in the identification of slow and fast oscillations. We also exhibit that short-time synchronization of complex networks can be understood with the help of perpetual motion of the network.