Bounds for the asymptotic order parameter of the stochastic Kuramoto model (Q526780)

The Kuramoto model describes how the phases of coupled oscillators evolve in time. Recent research into this subject produced necessary and sufficient conditions for reversibility by deriving some lower and upper bounds for the asymptotic order parameter, which involves modified Bessel functions of the first kind of order zero and one. The authors extend these results to modified Bessel functions of the first kind of arbitrary order employing some interesting new and recently discovered Turán-type inequalities for modified Bessel functions of the first kind. They also show that it is possible to obtain another approximation for the asymptotic order parameter by means of the Lagrange's inversion theorem and also a rational approximation.