3,045 research outputs found
Colored noise in oscillators. Phase-amplitude analysis and a method to avoid the Ito-Stratonovich dilemma
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 equivalent system subject to white Gaussian noise. A
description in terms of phase and amplitude deviation is given for the
transformed system. Using stochastic averaging technique, the equations are
reduced to a phase model that can be analyzed to characterize phase noise. We
find that phase noise is a drift-diffusion process, with a noise-induced
frequency shift related to the variance and to the correlation time of colored
noise. The proposed approach improves the accuracy of previous phase reduced
models
Lineshape distortion in a nonlinear auto-oscillator near generation threshold: Application to spin-torque nano-oscillators
The lineshape in an auto-oscillator with a large nonlinear frequency shift in
the presence of thermal noise is calculated. Near the generation threshold,
this lineshape becomes strongly non-Lorentzian, broadened, and asymmetric. A
Lorentzian lineshape is recovered far below and far above threshold, which
suggests that lineshape distortions provide a signature of the generation
threshold. The theory developed adequately describes the observed behavior of a
strongly nonlinear spin-torque nano-oscillator.Comment: 4 pages, 3 figure
Dynamics of Limit Cycle Oscillator Subject to General Noise
The phase description is a powerful tool for analyzing noisy limit cycle
oscillators. The method, however, has found only limited applications so far,
because the present theory is applicable only to the Gaussian noise while noise
in the real world often has non-Gaussian statistics. Here, we provide the phase
reduction for limit cycle oscillators subject to general, colored and
non-Gaussian, noise including heavy-tailed noise. We derive quantifiers like
mean frequency, diffusion constant, and the Lyapunov exponent to confirm
consistency of the result. Applying our results, we additionally study a
resonance between the phase and noise.Comment: main paper: 4 pages, 2 figure; auxiliary material: 5-7 pages of the
document, 1 figur
A Nanoscale Parametric Feedback Oscillator
We describe and demonstrate a new oscillator topology, the parametric feedback oscillator (PFO). The PFO paradigm is applicable to a wide variety of nanoscale devices and opens the possibility of new classes of oscillators employing innovative frequency-determining elements, such as nanoelectromechanical systems (NEMS), facilitating integration with circuitry and system-size reduction. We show that the PFO topology can also improve nanoscale oscillator performance by circumventing detrimental effects that are otherwise imposed by the strong device nonlinearity in this size regime
Effective long-time phase dynamics of limit-cycle oscillators driven by weak colored noise
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 sensitivity of the oscillator and the correlation
function of the noise, and are explicitly calculated for oscillators with
sinusoidal phase sensitivity functions driven by two typical colored Gaussian
processes. The results are verified by numerical simulations using several
types of stochastic or chaotic noise. The drift and diffusion coefficients of
oscillators driven by chaotic noise exhibit anomalous dependence on the
oscillator frequency, reflecting the peculiar power spectrum of the chaotic
noise.Comment: 16 pages, 6 figure
Stochastic resonance in electrical circuits—I: Conventional stochastic resonance.
Stochastic resonance (SR), a phenomenon in which a periodic signal in a nonlinear system can be amplified by added noise, is introduced and discussed. Techniques for investigating SR using electronic circuits are described in practical terms. The physical nature of SR, and the explanation of weak-noise SR as a linear response phenomenon, are considered. Conventional SR, for systems characterized by static bistable potentials, is described together with examples of the data obtainable from the circuit models used to test the theory
Colored Noise in Oscillators. Phase-Amplitude Analysis and a Method to Avoid the Itô-Stratonovich Dilemma
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 equivalent system subject to white Gaussian noise. A description in terms of phase and amplitude deviation is given for the transformed system. Using stochastic averaging technique, the equations are reduced to a phase model that can be analyzed to characterize phase noise. We find that phase noise is a drift-diffusion process, with a noise-induced frequency shift related to the variance and to the correlation time of colored noise. The proposed approach improves the accuracy of the previous phase reduced models
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