A quantitative proof that Kuramoto-Sakaguchi solutions converge exponentially fast to the unique synchronized equilibrium from generic initial data when the coupling strength is large, with a companion probability estimate for finite oscillator systems.
Stability of partially locked states in the Kuramoto model through Landau damping with Sobolev regularity
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abstract
The Kuramoto model is a mean-field model for the synchronisation behaviour of oscillators, which exhibits Landau damping. In a recent work, the nonlinear stability of a class of spatially inhomogeneous stationary states was shown under the assumption of analytic regularity. This paper proves the nonlinear Landau damping under the assumption of Sobolev regularity. The weaker regularity required the construction of a different more robust bootstrap argument, which focuses on the nonlinear Volterra equation of the order parameter.
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On the trend to global equilibrium for Kuramoto Oscillators
A quantitative proof that Kuramoto-Sakaguchi solutions converge exponentially fast to the unique synchronized equilibrium from generic initial data when the coupling strength is large, with a companion probability estimate for finite oscillator systems.