相关论文: Dynamics of Limit Cycle Oscillator Subject to Gene…

We formulate a phase-reduction method for a general class of noisy limit cycle oscillators and find that the phase equation is parametrized by the ratio between time scales of the noise correlation and amplitude relaxation of the limit…

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…

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 phase reduction method for limit cycle oscillators subjected to weak perturbations has significantly contributed to theoretical investigations of rhythmic phenomena. We here propose a generalized phase reduction method that is also…

This is a comment on a recent paper by Yoshimura and Arai [Phys. Rev. Lett. 101, 154101 (2008)] on phase reduction of noisy limit-cycle oscillators, in which the authors claimed that the conventional phase stochastic differential equation…

The phase reduction method is a dimension reduction method for weakly driven limit-cycle oscillators, which has played an important role in the theoretical analysis of synchro- nization phenomena. Recently, we proposed a generalization of…

We study the influence of telegraph noise on synchrony of limit cycle oscillators. Adopting the phase description for these oscillators, we derive the explicit expression for the Lyapunov exponent. We show that either for weak noise or…

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…

Oscillations and noise are ubiquitous in physical and biological systems. When oscillations arise from a deterministic limit cycle, entrainment and synchronization may be analyzed in terms of the asymptotic phase function. In the presence…

We study synchronization properties of general uncoupled limit-cycle oscillators driven by common and independent Gaussian white noises. Using phase reduction and averaging methods, we analytically derive the stationary distribution of the…

Synchronization of coupled oscillators is a paradigm for complexity in many areas of science and engineering. Any realistic network model should include noise effects. We present a description in terms of phase and amplitude deviation for…

Some limit theorems are proven for the linear oscillator with random coefficients. The asymptotic behaviour of the moments is studied in detail. The technique presented in this paper can be applied to general linear systems with noise and…

The output of oscillators is usually not stable over time. In particular, phase variations---or \emph{phase noise}---corrupts the oscillations. In this letter, we describe a circuit that designed to average the phase noise processes and…

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…

We study a large population of globally coupled phase oscillators subject to common white Gaussian noise and find analytically that the critical coupling strength between oscillators for synchronization transition decreases with an increase…

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…

We formulate a theory for the collective phase description of globally coupled noisy limit-cycle oscillators exhibiting macroscopic rhythms. Collective phase equations describing such macroscopic rhythms are derived by means of a two-step…

The synchronization of rhythms is ubiquitous in both natural and engineered systems, and the demand for data-driven analysis is growing. When rhythms arise from limit cycles, phase reduction theory shows that their dynamics are universally…

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…

Experimental realization and quantitative investigation of common-noise-induced synchronization of limit-cycle oscillations subject to random telegraph signals are performed using an electronic oscillator circuit. Based on our previous…