First Order Phase Transition Resulting from Finite Inertia in Coupled Oscillator Systems

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Abstract
We analyze the collective behavior of a set of coupled damped driven pendula with finite (large) inertia, and show that the synchronization of the oscillators exhibits a first order phase transition synchronization onset, substantially different from the second order transition obtained in the case of no inertia. There is hysteresis between two macroscopic states, a weakly and a strongly coherent synchronized state, depending on the coupling and the initial state of the oscillators. A self-consistent theory is shown to determine these cooperative phenomena and to predict the observed numerical data in specific examples.

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