Related papers: A generalization of the Leeson effect
We report on the measurement and characterization of power to frequency conversion in the resonant mode of a cryogenic sapphire loaded cavity resonator, which is used as the frequency discriminating element of a loop oscillator circuit.…
Phase oscillators are a common starting point for the reduced description of many single neuron models that exhibit a strongly attracting limit cycle. The framework for analysing such models in response to weak perturbations is now…
High-stability quartz oscillators are needed in a number of space applications. A short-term stability of parts in 10^{-14} [Allan deviation \sigma y(\tau) ] is sometimes required, for integration time \tau of approximately 1-10 s. The…
This article explains phase noise, jitter, and some slower phenomena in digital integrated circuits, focusing on high-demanding, noise-critical applications. We introduce the concept of phase type and time type phase noise. The rules for…
This paper addresses the analysis of oscillator phase-noise effects on the self-interference cancellation capability of full-duplex direct-conversion radio transceivers. Closed-form solutions are derived for the power of the residual…
The Duffing oscillator is a nonlinear extension of the ubiquitous harmonic oscillator and as such plays an outstanding role in science and technology. Experimentally, the system parameters are determined by a measurement of its response to…
We study the noise characteristics of stochastic oscillations in protein number dynamics of simple genetic oscillatory systems. Using the three-component negative feedback transcription regulatory system called the repressilator as a…
Oscillatory systems arise in the different science fields. Complex mathematical formulations with differential equations have been proposed to model the dynamics of these systems. While they have the advantage of having a direct…
The phase diffusion in a self-sustained oscillator, which produces oscillator's spectral linewidth, is inherently governed by a nonlinear Langevin equation. Over past 40 years, the equation has been treated with linear approximation,…
Nonlinear damping, the change in damping rate with the amplitude of oscillations plays an important role in many electrical, mechanical and even biological oscillators. In novel technologies such as carbon nanotubes, graphene membranes or…
We examine the weak quantum noise limit of Wigner equation for phase space distribution functions. It has been shown that the leading order quantum noise described in terms of an auxiliary Hamiltonian manifests itself as an additional…
We present a detailed theoretical discussion of the effects of ubiquitous laser noise on cooling and the coherent dynamics in opto-mechanical systems. Phase fluctuations of the driving laser induce modulations of the linearized…
We address two aspects of the dynamics of the forced Duffing oscillator which are relevant to the technology of micromechanical devices and, at the same time, have intrinsic significance to the field of nonlinear oscillating systems. First,…
Autoresonance is a phase locking phenomenon occurring in nonlinear oscislatory system, which is forced by oscillating perturbation. Many physical applicatcons of the autoresonance are known in nonlenear physics. The essence of the…
Motivated by recent surprising experimental results for the noise output of superconducting microfabricated resonators used in quantum computing applications and astronomy, we develop a fully quantum theoretical model to describe quantum…
We develop a method to investigate the effect of noise timescales on the first-passage time of nonlinear oscillators. Using Fredholm theory, we derive an exact integral equation for the mean event rate of a leaky-integrate-and-fire…
The interaction between the fractional order parameter and the damping parameter can play a relevant role for introducing different dynamical behaviors in a physical system. Here, we study the Duffing oscillator with a fractional damping…
Phase noise and frequency (in)stability both describe the fluctuation of stable periodic signals, from somewhat different standpoints. Frequency is unique compared to other domains of metrology, in that its fluctuations of interest span at…
Studies about the constructive aspects of noise and fluctuations in different non-linear systems have shown that the addition of external noise to systems with an intrinsic noise may result in a less noisy response. Recently, the…
The harmonic oscillator is a powerful model that can appear as a limit case when examining a nonlinear system. A well known fact is, that without driving, the inclusion of a friction term makes the origin of the phase space -- which is a…