Related papers: Phase coherence in an ensemble of uncoupled limit-…
Populations of uncoupled limit-cycle oscillators receiving common random impulses show various types of phase-coherent states, which are characterized by the distribution of phase differences between pairs of oscillators. We develop a…
The mechanism of phase synchronization between uncoupled limit-cycle oscillators induced by common external impulsive forcing is analyzed. By reducing the dynamics of the oscillator to a random phase map, it is shown that phase…
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)…
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…
Ensembles of phase-oscillators are known to exhibit a variety of collective regimes. Here, we show that a simple mean-field model involving two heterogenous populations of pulse-coupled oscillators, exhibits, in the strong-coupling limit, a…
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…
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…
The collective phase response to a macroscopic external perturbation of a population of interacting nonlinear elements exhibiting collective oscillations is formulated for the case of globally-coupled oscillators. The macroscopic phase…
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…
We introduce a stochastic model of coupled genetic oscillators in which chains of chemical events involved in gene regulation and expression are represented as sequences of Poisson processes. We characterize steady states by their…
We address the problem of steering the phase distribution of oscillators all receiving the same control input to a given target distribution. In a large population limit, the distribution of oscillators can be described by a probability…
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…
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…
The collective behavior of the ensembles of coupled nonlinear oscillator is one of the most interesting and important problems in modern nonlinear dynamics. In this paper, we study rotational dynamics, in particular space-time structures,…
We present an approach which enables to identify phase synchronization in coupled chaotic oscillators without having to explicitly measure the phase. We show that if one defines a typical event in one oscillator and then observes another…
Shared upstream dynamical processes are frequently the source of common inputs in various physical and biological systems. However, due to finite signal transmission speeds and differences in the distance to the source, time shifts between…
Random perturbations applied in tandem to an ensemble of oscillating objects can synchronize their motion. We study multiple copies of an arbitrary dynamical system in a stable limit cycle, described via a standard phase reduction picture.…
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 study synchronization phenomenon in a self-correcting population of noisy phase oscillators with randomly distributed natural frequencies. In our model each oscillator stochastically switches its phase to the ensemble-averaged value…
Coupled oscillators have been used to study synchronization in a wide range of social, biological, and physical systems, including pedestrian-induced bridge resonances, coordinated lighting up of firefly swarms, and enhanced output peak…