Related papers: Phase reduction approach to synchronization of non…
We present an approach which enables to state about the existence of phase synchronization in coupled chaotic oscillators without having to measure the phase. This is done by observing the oscillators at special times, and analyzing whether…
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…
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…
For many natural and engineered systems, a central function or design goal is the synchronization of one or more rhythmic or oscillating processes to an external forcing signal, which may be periodic on a different time-scale from the…
A rationale is provided for the emergence of synchronization in a system of coupled oscillators in a stick-slip motion. The single oscillator has a limit cycle in a region of the state space for each parameter set beyond the supercritical…
Theoretical studies of synchronization are usually based on models of coupled phase oscillators which, when isolated, have constant angular frequency. Stochastic discrete versions of these uniform oscillators have also appeared in the…
Synchronization is a phenomenon where interacting particles lock their motion and display non-trivial dynamics. Despite intense efforts studying synchronization in systems without clear classical limits, no comprehensive theory has been…
Spontaneous synchronization between coupled periodic systems occur in a wealth of classical physical setups. Here, we show theoretically that the phase of two distinct quantum harmonic oscillators spontaneously when they are strongly…
This study explores a method to characterize temporal structure of intermittent phase locking in oscillatory systems. When an oscillatory system is in a weakly synchronized regime away from a synchronization threshold, it spends most of the…
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.…
The behaviors of coupled oscillators, each of which has periodic motion with random natural frequency in the absence of coupling, are investigated. Some novel collective phenomena are revealed. At the onset of instability of the…
Nonlinear oscillators can mutually synchronize when they are driven by common external impulses. Two important scenarios are (i) synchronization resulting from phase locking of each oscillator to regular periodic impulses and (ii)…
We develop a formalism to analyze the behaviour of pulse--coupled identical phase oscillators with a specific attention devoted to the onset of partial synchronization. The method, which allows describing the dynamics both at the…
Different types of synchronization states are found when non-linear chemical oscillators are embedded into an active medium that interconnects the oscillators but also contributes to the system dynamics. Using different theoretical tools,…
In this paper we use the parameterization method to provide a complete description of the dynamics of an $n$-dimensional oscillator beyond the classical phase reduction. The parameterization method allows, via efficient algorithms, to…
The phase-space of a simple synchronization model is thoroughly investigated. The model considers two-mode stochastic oscillators, coupled through a pulse-like interaction controlled by simple optimization rules. A complex phase space is…
It is well known from classical physics that weakly coupled self-sustained oscillators may spontaneously lock their phases. Just like classical synchronization is known to break down due to noise induced phase slips, we show here how the…
We propose a method for optimizing mutual coupling functions to achieve fast and global synchronization between a pair of weakly coupled limit-cycle oscillators. Our method is based on phase reduction that provides a concise low-dimensional…
A system of coupled oscillators on an arbitrary graph is locally driven by the tendency to mutual synchronization between nearby oscillators, but can and often exhibit nonlinear behavior on the whole graph. Understanding such nonlinear…
There are three key factors of a system of coupled oscillators that characterize the interaction among them: coupling (how to affect), delay (when to affect) and topology (whom to affect). For each of them, the existing work has mainly…