Related papers: Comment on "Asymptotic Phase for Stochastic Oscill…
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…
Thomas and Lindner (2014, Phys.Rev.Lett.) defined an asymptotic phase for stochastic oscillators as the angle in the complex plane made by the eigenfunction, having a complex eigenvalue with a least negative real part, of the backward…
The asymptotic phase is a fundamental quantity for the analysis of deterministic limit-cycle oscillators, and generalized definitions of the asymptotic phase for stochastic oscillators have also been proposed. In this article, we show that…
In his Comment [arXiv:1501.02126 (2015)] on our recent paper [Phys. Rev. Lett., v. 113, 254101 (2014)], Pikovsky compares two methods for defining the "phase" of a stochastic oscillator. We reply to his Comment by showing that neither…
Stochastic oscillators play a prominent role in different fields of science. Their simplified description in terms of a phase has been advocated by different authors using distinct phase definitions in the stochastic case. One notion of…
We propose a definition of the asymptotic phase for quantum nonlinear oscillators from the viewpoint of the Koopman operator theory. The asymptotic phase is a fundamental quantity for the analysis of classical limit-cycle oscillators, but…
Oscillators are ubiquitous in nature, and usually associated with the existence of an asymptotic phase that governs the long-term dynamics of the oscillator. % We show that asymptotic phase can be estimated using a carefully chosen series…
We introduce an invariant phase description of stochastic oscillations by generalizing the concept of standard isophases. The average isophases are constructed as sections in the state space, having a constant mean first return time. The…
Several definitions of phase have been proposed for stochastic oscillators, among which the mean-return-time phase and the stochastic asymptotic phase have drawn particular attention. Quantitative comparisons between these two definitions…
An effective description of a general class of stochastic phase oscillators is presented. For this, the effective phase velocity is defined either by invariant probability density or via first passage times. While the first approach…
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,…
For an attracting periodic orbit (limit cycle) of a deterministic dynamical system, one defines the isochron for each point of the orbit as the cross-section with fixed return time under the flow. Equivalently, isochrons can be…
The purpose of this article is to describe the singularities of one-dimensional oscillatory integrals, whose phases have a certain singularity, in the form of an asymptotic expansion. In the case of the Laplace integral, an analogous result…
Phase reduction is an important tool for studying coupled and driven oscillators. The question of how to generalize phase reduction to stochastic oscillators remains actively debated. In this work, we propose a method to derive a…
We present a phase autoencoder that encodes the asymptotic phase of a limit-cycle oscillator, a fundamental quantity characterizing its synchronization dynamics. This autoencoder is trained in such a way that its latent variables directly…
In plasma turbulence theory, due to the complexity of the system with many non-linearly interacting waves, the dynamics of the phases is often disregarded and the so-called random-phase approximation (RPA) is used assuming the existence of…
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…
Stochastic oscillations are ubiquitous in many systems. For deterministic systems, the oscillator's phase has been widely used as an effective one-dimensional description of a higher dimensional dynamics, particularly for driven or coupled…
The parameterization method (PM) provides a broad theoretical and numerical foundation for computing invariant manifolds of dynamical systems. PM implements a change of variables in order to represent trajectories of a system of ordinary…
This paper presents a phase description of chaotic dynamics for the study of chaotic phase synchronization. A prominent feature of the proposed description is that it systematically incorporates the dynamics of the non-phase variables…