Related papers: Direct extraction of phase dynamics from fluctuati…

Since many physical laws -- from classical mechanics to electromagnetism -- are formulated as two-body interactions, the same perspective naturally extends to biological and social dynamics. Here we focus on rhythmic phenomena, where phase…

There is enormous interest -- both mathematically and in diverse applications -- in understanding the dynamics of coupled oscillator networks. The real-world motivation of such networks arises from studies of the brain, the heart, ecology,…

A large variety of rhythms are observed in nature. Rhythms such as electroencephalogram signals in the brain can often be regarded as interacting. In this study, we investigate the dynamical properties of rhythmic systems in two populations…

The entrainment between weakly-coupled nonlinear oscillators, as well as between complex signals such as those representing physiological activity, is frequently assessed in terms of whether a stable relationship is detectable between the…

We present a novel approach for recovery of the directional connectivity of a small oscillator network by means of the phase dynamics reconstruction from multivariate time series data. The main idea is to use a triplet analysis instead of…

We develop a numerical approach to reconstruct the phase dynamics of driven or coupled self-sustained oscillators. Employing a simple algorithm for computation of the phase of a perturbed system, we construct numerically the equation for…

Models of coupled oscillators are useful in describing a wide variety of phenomena in physics, biology and economics. These models typically rest on the premise that the oscillators are weakly coupled, meaning that amplitudes can be assumed…

Weakly coupled oscillators are used throughout the physical sciences, particularly in mathematical neuroscience to describe the interaction of neurons in the brain. Systems of weakly coupled oscillators have a well-known decomposition to a…

Rhythmic activity is ubiquitous in biological systems from the cellular to organism level. Reconstructing the instantaneous phase is the first step in analyzing the essential mechanism leading to a synchronization state from the observed…

A method is presented for tracing the locus of a specific peak in the frequency response under variation of a parameter. It is applicable to periodic, steady-state vibrations of harmonically forced nonlinear mechanical systems. It operates…

An adiabatic-connection fluctuation-dissipation theorem approach based on a range separation of electron-electron interactions is proposed. It involves a rigorous combination of short-range density functional and long-range random phase…

We propose a reduction scheme for a system constituted by two coupled harmonically-bound Brownian oscillators. We reduce the description by constructing a lower dimensional model which inherits some of the basic features of the original…

Networks of coupled phase oscillators are one of the most studied dynamical systems with numerous applications in physics, chemistry, biology, and engineering. Their behaviour is often characterized by the emergence of various partially…

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…

The tools of weakly coupled phase oscillator theory have had a profound impact on the neuroscience community, providing insight into a variety of network behaviours ranging from central pattern generation to synchronisation, as well as…

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…

We present a method to infer network connectivity from collective dynamics in networks of synchronizing phase oscillators. We study the long-term stationary response to temporally constant driving. For a given driving condition, measuring…

We present a phase-amplitude reduction framework for analyzing collective oscillations in networked dynamical systems. The framework, which builds on the phase reduction method, takes into account not only the collective dynamics on the…

Spontaneous oscillations induced by time delays are observed in many real-world systems. Phase reduction theory for limit-cycle oscillators described by delay-differential equations (DDEs) has been developed to analyze their synchronization…

Time-series analysis is critical for a diversity of applications in science and engineering. By leveraging the strengths of modern gradient descent algorithms, the Fourier transform, multi-resolution analysis, and Bayesian spectral…