Remarks on the nonlinear stability of the Kuramoto-Sakaguchi equation

We present a nonlinear stability estimate of the incoherent solution to the Kuramoto-Sakaguchi equation using energy estimates. Our global stability analysis does not require the amplitude of the solution to be small, as long as the ratio of diffusion strength to coupling strength is sufficiently large. We also show that the Kuramoto-Sakaguchi equation is L2-contractive in the perturbed regime of the incoherent solution. Moreover, we establish the L∞-convergence in any finite time interval from the Kuramoto-Sakaguchi equation to the Kuramoto equation as the diffusion coefficient goes to zero.