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We study populations of oscillators, all-to-all coupled by means of quencheddisordered phase shifts. While there is no traditional synchronizationtransition with a nonvanishing Kuramoto order parameter, the systemdemonstrates a specific order as the coupling strength increases. This order ischaracterized by partial phase locking, which is put into evidence by theintroduced correlation order parameter and via frequency entrainment.Simulations with phase oscillators, Stuart-Landau oscillators, and chaoticRoessler oscillators demonstrate similar scaling of the correlation orderparameter with the coupling and the system size and also similar behavior ofthe frequencies with maximal entrainment at some finite coupling.

Dynamics of oscillator populations with disorder in the coupling phase shifts