Related papers: Asymptotic Phase for Stochastic Oscillators
Synchronization of quantum nonlinear oscillators has attracted much attention recently. To characterize the quantum oscillatory dynamics, we recently proposed a fully quantum-mechanical definition of the asymptotic phase, which is a key…
In this tutorial, three examples of stochastic systems are considered: A strongly-damped oscillator, a weakly-damped oscillator and an undamped oscillator (integrator) driven by noise. The evolution of these systems is characterized by the…
We introduce a stochastic model for the determination of phase noise in optoelectronic oscillators. After a short overview of the main results for the phase diffusion approach in autonomous oscillators, an extension is proposed for the case…
In this paper we present a theory that predicts the phase noise characteristics of self-sustained optomechanical oscillators. By treating the cavity optomechanical system as a feedback loop consisting of an optical cavity and a mechanical…
For stochastic systems with nonvanishing noise, i.e., at the desired state the noise port does not vanish, it is impossible to achieve the global stability of the desired state in the sense of probability. This bad property also leads to…
Numerous biological and microscale systems exhibit synchronization in noisy environments. The theory of such noisy oscillators and their synchronization has been developed and experimentally demonstrated, but inferring the noise intensity…
We give an exact result about the asymptotic limit of an oscillatory integral whose phase contains a certain flat term. Corresponding to the real analytic phase case, one can see an essential difference in the behavior of the above…
We point out that the phase reduction of stochastic limit cycle oscillators has been done incorrectly in the literature. We present a correct phase reduction method for oscillators driven by weak external white Gaussian noises. Numerical…
Many systems in physics, chemistry and biology exhibit oscillations with a pronounced random component. Such stochastic oscillations can emerge via different mechanisms, for example linear dynamics of a stable focus with fluctuations,…
Periodic recurrence is a prominent behavioural of many biological phenomena, including cell cycle and circadian rhythms. Although deterministic models are commonly used to represent the dynamics of periodic phenomena, it is known that they…
We study a noisy oscillator with pulse delayed feedback, theoretically and in an electronic experimental implementation. Without noise, this system has multiple stable periodic regimes. We consider two types of noise: i) phase noise acting…
Systems of dynamical elements exhibiting spontaneous rhythms are found in various fields of science and engineering, including physics, chemistry, biology, physiology, and mechanical and electrical engineering. Such dynamical elements are…
In this paper we present a general framework in which one can rigorously study the effect of spatio-temporal noise on traveling waves, stationary patterns and oscillations that are invariant under the action of a finite-dimensional set of…
We introduce a new method for reducing phase noise in oscillators, thereby improving their frequency precision. The noise reduction device consists of a pair of coupled nonlinear resonating elements that are driven parametrically by the…
An autonomous system of ordinary differential equations describing nonlinear oscillations on the plane is considered. The influence of time-dependent perturbations decaying at infinity in time is investigated. It is assumed that the…
We present a method for analyzing the phase noise of oscillators based on feedback driven high quality factor resonators. Our approach is to derive the phase drift of the oscillator by projecting the stochastic oscillator dynamics onto a…
One notion of phase for stochastic oscillators is based on the mean return-time (MRT): a set of points represents a certain phase if the mean time to return from any point in this set to this set after one rotation is equal to the mean…
We show that a wide class of uncoupled limit cycle oscillators can be in-phase synchronized by common weak additive noise. An expression of the Lyapunov exponent is analytically derived to study the stability of the noise-driven…
The combined influence of oscillatory excitations and multiplicative stochastic perturbations of white noise type on isochronous systems in the plane is investigated. It is assumed that the intensity of perturbations decays with time and…
We study the stability of a stochastic oscillator whose frequency is a random process with finite time memory represented by an Ornstein-Uhlenbeck noise. This system undergoes a noise-induced bifurcation when the amplitude of the noise…