ISSN:
1572-9613
Keywords:
Nonlinear oscillator
;
synchronization
;
phase transition
;
mean-field model
;
bifurcation
;
collective phenomena
;
phase locking
Source:
Springer Online Journal Archives 1860-2000
Topics:
Physics
Notes:
Abstract We analyze a mean-field model of coupled oscillators with randomly distributed frequencies. This system is known to exhibit a transition to collective oscillations: for small coupling, the system is incoherent, with all the oscillators running at their natural frequencies, but when the coupling exceeds a certain threshold, the system spontaneously synchronizes. We obtain the first rigorous stability results for this model by linearizing the Fokker-Planck equation about the incoherent state. An unexpected result is that the system has pathological stability properties: the incoherent state is unstable above threshold, butneutrally stable below threshold. We also show that the system is singular in the sense that its stability properties are radically altered by infinitesimal noise.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01029202
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