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First Order Phase Transition Resulting from Finite Inertia in Coupled Oscillator Systems
Hisa-Aki Tanaka and Allan J. Lichtenberg
Physical Review Letters, 1997.
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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