Related papers: Phase reduction of stochastic limit cycle oscillat…
We study the noise-induced escape from a stable limit cycle of a non-gradient dynamical system driven by a small additive noise. The fact that the optimal transition path in this case is infinitely long imposes a severe numerical challenge…
Optimization of mutual synchronization between a pair of limit-cycle oscillators with weak symmetric coupling is considered in the framework of the phase reduction theory. By generalizing a previous study on the optimization of…
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…
Time, and equivalently frequency, is the most precisely measured physical quantity. It is therefore inevitable that virtually all domains of engineering and physics need reference oscillators. The oscillator noise can be decomposed into…
Collective oscillations of lattices of locally-coupled chaotic Roessler oscillators are studied with regard to the dynamical scaling of their phase interfaces. Using analogies with the complex Ginzburg-Landau and the Kardar-Parisi-Zhang…
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…
The dynamics of an ensemble of $N$ weakly coupled limit-cycle oscillators can be captured by their $N$ phases using standard phase reduction techniques. However, it is a phenomenological fact that all-to-all strongly coupled limit-cycle…
An overview is given on two representative methods of dynamical reduction known as center-manifold reduction and phase reduction. These theories are presented in a somewhat more unified fashion than the theories in the past. The target…
We make a short review about the synchronization in coupled phase oscillator models. Next, we study the common-noise-induced synchronization among active rotators. At an intermediate noise strength, the noise-induced synchronization takes…
A new type of noised induced phase transitions is proposed. It occurs in noisy systems with dynamical traps. Dynamical traps are regions in the phase space where the regular forces are depressed substantially. By way of an example, a simple…
Given the high dimensionality and underlying complexity of many oscillatory dynamical systems, phase reduction is often an imperative first step in control applications where oscillation timing and entrainment are of interest.…
Reproducibility of a noisy limit-cycle oscillator driven by a random piecewise constant signal is analyzed. By reducing the model to random phase maps, it is shown that the reproducibility of the limit cycle generally improves when the…
Cavity opto-mechanical cooling via radiation pressure dynamical backaction enables ground state cooling of mechanical oscillators, provided the laser exhibits sufficiently low phase noise. Here, we investigate and measure the excess phase…
We have found that a novel type of entrainment occurs in two nonidentical limit cycle oscillators subjected to a common external white Gaussian noise. This entrainment is anomalous in the sense that the two oscillators have different mean…
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…
We investigate a ring of $N$ FitzHugh--Nagumo elements coupled in \emph{phase-repulsive} fashion and submitted to a (subthreshold) common oscillatory signal and independent Gaussian white noises. This system can be regarded as a reduced…
Optimal entrainment of a quantum nonlinear oscillator to a periodically modulated weak harmonic drive is studied in the semiclassical regime. By using the semiclassical phase reduction theory recently developed for quantum nonlinear…
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…
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…
Phase reduction is a general tool widely used to describe forced and interacting self-sustained oscillators. Here we explore the phase coupling functions beyond the usual first-order approximation in the strength of the force. Taking the…