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The synchronization analysis of amplitude oscillators in this paper differs from analyses that incorporate cubic nonlinearities (see, for example, and) in that here we consider phase, not amplitude, synchronization. Whereas in these other models the amplitude order parameter ρ (1/N) | j=1 N ψj | = (1/N) | j=1 N Rj ei θj | has an upper bound of 1 and is used as a measure of amplitude synchronization, in the present model ρ has no upper bound and the amplitude is not a free variable. Furthermore, in the linear model presented in this paper the amplitude decays for systems of uncoupled oscillators, unlike in the models with cubic nonlinearities.
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Uniformly coupled continuum systems-those that have an analytic Kuramoto solution Eq. 3 -with uniform characteristic frequency distributions also exhibit this absence of partially locked states.
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Uniformly coupled continuum systems-those that have an analytic Kuramoto solution Eq. 3 -with uniform characteristic frequency distributions also exhibit this absence of partially locked states.
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