Related papers: A generalization of the Leeson effect

This paper investigates the effect of oscillator phase noise and channel variations due to fading on the performance of communication systems at frequency bands higher than 10GHz. Phase noise and channel models are reviewed and…

We theoretically study the frequency stability of an opto-mechanical radio frequency oscillator based on resonant interaction of two optical and one mechanical modes of the same optical microcavity. A generalized expression for the phase…

We present recent results on noise-induced transitions in a nonlinear oscillator with randomly modulated frequency. The presence of stochastic perturbations drastically alters the dynamical behaviour of the oscillator: noise can wash out a…

Theoretical models that describe oscillations in biological systems are often either a limit cycle oscillator, where the deterministic nonlinear dynamics gives sustained periodic oscillations, or a noise-induced oscillator, where a fixed…

This paper deals with the phase noise affecting communication systems, where local oscillators are employed to obtain reference signals for carrier and timing synchronizations. The most common discrete-time phase noise channel model is…

We consider classical nonlinear oscillators on hexagonal lattices. When the coupling between the elements is repulsive, we observe coexisting states, each one with its own basin of attraction. These states differ by their degree of…

Stochastic resonance is a general phenomenon usually observed in one-dimensional, amplitude modulated, bistable systems.We show experimentally the emergence of phase stochastic resonance in the bidimensional response of a forced…

An effective description of a general class of stochastic phase oscillators is presented. For this, the effective phase velocity is defined either by invariant probability density or via first passage times. While the first approach…

This article deals with the erratic and inconsistent phase-noise spectra often seen in low-noise oscillators, whose floor is of the order of $-180$ dBc/Hz or less. Such oscillators are generally measured with two-channel instruments based…

We consider the fractional oscillator being a generalization of the conventional linear oscillator in the framework of fractional calculus. It is interpreted as an ensemble average of ordinary harmonic oscillators governed by stochastic…

A description in terms of phase and amplitude variables is given, for nonlinear oscillators subject to white Gaussian noise described by It\^o stochastic differential equations. The stochastic differential equations derived for the…

We analyze the amplitude and phase noise of limit-cycle oscillations in a mechanical resonator coupled parametrically to an optical cavity driven above its resonant frequency. At a given temperature the limit-cycle oscillations have lower…

A harmonic oscillator under influence of the noise is a basic model of various physical phenomena. Under Gaussian white noise the position and velocity of the oscillator are independent random variables which are distributed according to…

The diffusive behavior of a harmonic oscillator driven by a Mittag-Leffler noise is studied. Using Laplace analysis we derive exact expressions for the relaxation functions of the particle in terms of generalized Mittag-Leffler functions…

A new mechanism of low frequency (1/f-like) noise generation is described and analyzed. It is attributed to higher frequency asymmetric resonance modes, which are stimulated by a random factor, e.g. due to thermal excitation.…

Mechanical resonators are widely used as precision clocks and sensitive detectors that rely on the stability of their eigenfrequencies. The phase noise is determined by different factors ranging from thermal noise and frequency noise of the…

The synchronized phase of globally coupled nonlinear oscillators subject to noise fluctuations is studied by means of a new analytical approach able to tackle general couplings, nonlinearities, and noise temporal correlations. Our results…

In this report, we lay the foundation for amplitude noise and phase noise analysis in nonlinear devices. We build a theoretical framework that helps us to analyze extremely difficult problems which include both nonlinearity and noise of…

We investigate the effect of time-correlated noise on the phase fluctuations of nonlinear oscillators. The analysis is based on a methodology that transforms a system subject to colored noise, modeled as an Ornstein-Uhlenbeck process, into…

An effective white-noise Langevin equation is derived that describes long-time phase dynamics of a limit-cycle oscillator subjected to weak stationary colored noise. Effective drift and diffusion coefficients are given in terms of the phase…