Related papers: Phase Reduction and Synchronization of Coupled Noi…
Effect of noise in inducing order on various chaotically evolving systems is reviewed, with special emphasis on systems consisting of coupled chaotic elements. In many situations it is observed that the uncoupled elements when driven by…
We study a noisy oscillator with pulse delayed feedback, theoretically and in an electronic experimental implementation. Without noise, this system has multiple stable periodic regimes. We consider two types of noise: i) phase noise acting…
We describe synchronization transitions in an ensemble of globally coupled phase oscillators with a bi-harmonic coupling function, and two sources of disorder - diversity of intrinsic oscillatory frequencies and external independent noise.…
The theoretical description of synchronization phenomena often relies on coupled units of continuous time noisy Markov chains with a small number of states in each unit. It is frequently assumed, either explicitly or implicitly, that…
We formulate a phase-reduction method for a general class of noisy limit cycle oscillators and find that the phase equation is parametrized by the ratio between time scales of the noise correlation and amplitude relaxation of the limit…
The effects of disorder in external forces on the dynamical behavior of coupled nonlinear oscillator networks are studied. When driven synchronously, i.e., all driving forces have the same phase, the networks display chaotic dynamics. We…
A geometric approach is introduced for understanding the phenomenon of phase synchronization in coupled nonlinear systems in the presence of additive noise. We show that the emergence of cooperative behaviour through a change of stability…
We present a method for reconstructing resonant interactions in weakly coupled phase oscillator systems from noisy time series. Instead of attempting to recover the full phase equations, which may be non-identifiable in the presence of…
We consider a population of globally coupled oscillators driven by common noise. By applying the Ott-Antonsen ansatz and by averaging over the fast oscillations, we obtain analytically tractable equations for the noisy evolution of the…
We study the properties of large systems of globally coupled oscillators in the presence of noise. When the distribution of the natural frequencies of the oscillators is bimodal and its analytical continuation in the complex plane has only…
Synchronized neural spiking is associated with many cognitive functions and thus, merits study for its own sake. The analysis of neural synchronization naturally leads to the study of repetitive spiking and consequently to the analysis of…
The dynamical control of energy transfer between interacting systems is fundamental in diverse applications related to physical, electronic and chemical processes. Recent developments show that noise may enhance or suppress power transfer…
Physiological networks are usually made of a large number of biological oscillators evolving on a multitude of different timescales. Phase oscillators are particularly useful in the modelling of the synchronization dynamics of such systems.…
The study of synchronization among genetic oscillators is essential for the understanding of the rhythmic phenomena of living organisms at both molecular and cellular levels. Genetic networks are intrinsically noisy due to natural random…
Synchronization is a widespread phenomenon observed in physical, biological, and social networks, which persists even under the influence of strong noise. Previous research on oscillators subject to common noise has shown that noise can…
Many networks must maintain synchrony despite the fact that they operate in noisy environments. Important examples are stochastic inertial oscillators, which are known to exhibit fluctuations with broad tails in many applications, including…
The phenomenon of frequency and phase synchronization in stochastic systems requires a revision of concepts originally phrased in the context of purely deterministic systems. Various definitions of an instantaneous phase are presented and…
The synchronization stability of a complex network system of coupled phase oscillators is discussed. In case the network is affected by disturbances, a stochastic linearized system of the coupled phase oscillators may be used to determine…
We introduce an extension to the standard reduction of oscillatory systems to a single phase variable. The standard reduction is often insufficient, particularly when the oscillations have variable amplitude and the magnitude of each…
The phase response curve (PRC) is an important measure representing the interaction between oscillatory elements. To understand synchrony in biological systems, many research groups have sought to measure PRCs directly from biological cells…