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The Kuramoto model is a paradigm to describe the dynamics of nonlinear oscillators under the influence of external perturbations or couplings. It is based on the idea to reduce the state equations to a scalar differential equation, that defines the time evolution for the phase of the oscillator. In this paper we discuss the reduction procedure for nonlinear oscillators subject to stochastic perturbations...
We discuss the effect of the estimation of the amplitude variations on the noise-induced frequency shift in nonlinear oscillators. The analysis is based on a general reduction approach to a phase macromodel making use of the Itô interpretation of the stochastic differential equations representing noisy autonomous systems. We show that a significant improvement of the accuracy can be obtained by using...
We present a novel phase-amplitude model for noisy oscillators described by Itô stochastic differential equations. The model is completely rigorous and it holds for any value of the noise intensity. The phase and amplitude equations depend on the choice of an appropriate set of basis vectors. We show that using Floquet's basis, a phase-amplitude description is obtained analogous to others, previously...
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