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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…
We propose a method for controlling synchronization patterns of limit-cycle oscillators by common noisy inputs, i.e., by utilizing noise-induced synchronization. Various synchronization patterns, including fully synchronized and clustered…
From the flashes of fireflies to Josephson junctions and power infrastructure, networks of coupled phase oscillators provide a powerful framework to describe synchronization phenomena in many natural and engineered systems. Most real-world…
We investigate synchronization in complex networks of noisy phase oscillators. We find that, while too weak a coupling is not sufficient for the whole system to synchronize, too strong a coupling induces a nontrivial type of phase slip…
We consider networks of coupled stochastic oscillators. When coupled we find strong collective oscillations, while each unit remains stochastic. In the limit (N\to \infty) we derive a system of integro-delay equations and show analytically…
A unified framework for analyzing generalized synchronization in coupled chaotic systems from data is proposed. The key of the proposed approach is the use of the kernel methods recently developed in the field of machine learning. Several…
Given two unidirectionally coupled nonlinear systems, we speak of generalized synchronization when the responder \textquotedblleft follows\textquotedblright\ the driver. Mathematically, this situation is implemented by a map from the driver…
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…
We theoretically investigate collective phase synchronization between interacting groups of globally coupled noisy identical phase oscillators exhibiting macroscopic rhythms. Using the phase reduction method, we derive coupled collective…
We experimentally demonstrate and numerically simulate a new adaptive method to maintain synchronization between coupled nonlinear chaotic oscillators, when the coupling between the systems is unknown and time-varying (e.g., due to…
Coupled oscillators are among the simplest composite quantum systems in which the interplay of entanglement and interaction may be explored. We examine the effects of coupling on fluctuations of the coordinates and momenta of the…
The phenomenon of synchronization, where entities exhibit stable oscillations with aligned frequencies and phases, has been detected in diverse areas of natural science. It plays a crucial role in achieving frequency locking in multiple…
For finite-dimensional quantum systems, such as qubits, a well established strategy to protect such systems from decoherence is dynamical decoupling. However many promising quantum devices, such as oscillators, are infinite dimensional, for…
Generalized synchronization is plausibly the most complex form of synchronization. Previous studies have revealed the existence of weak or strong forms of generalized synchronization depending on the multi- or mono-valued nature of the…
The phase oscillator model with global coupling is extended to the case of finite-range nonlocal coupling. Under suitable conditions, peculiar patterns emerge in which a quasi-continuous array of identical oscillators separates sharply into…
We consider models of identical pulse-coupled oscillators with global interactions. Previous work showed that under certain conditions such systems always end up in sync, but did not quantify how small clusters of synchronized oscillators…
Understanding complex systems which exhibit desynchronization as an emergent property should have important implications, particularly in treating neurological disorders and designing efficient communication networks. Here were demonstrate…
This paper proposes a novel method to achieve and preserve synchronization for a set of connected heterogeneous Van der Pol oscillators. Unlike the state-of-the-art synchronization methods, in which a large coupling gain is applied to…
We show that a system is uniformly accelerated if and only if all of the clocks in the system can be synchronized to each other, and the clocks will remain synchronized as long as the acceleration remains uniform. In particular, it is…
In this paper we report for the first time on the necessity of the refinement of the concept of generalized chaotic synchronization. We show that the state vectors of the interacting chaotic systems being in the generalized synchronization…