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Populations of flashing fireflies, claps of applauding audience, cells of cardiac and circadian pacemakers reach synchrony via event-triggered interactions, referred to as pulse couplings. Synchronization via pulse coupling is widely used…
Synchronization is ubiquitous in nature, which is mathematically described by coupled oscillators. Synchronization strongly depends on the interaction network, and the network plays a crucial role in controlling the dynamics. To understand…
Synchronization is one of the paradigmatic phenomena in the study of complex systems. It has been explored theoretically and experimentally mostly to understand natural phenomena, but also in view of technological applications. Although…
It is often conjectured that quantum synchronisation and entanglement are two independent properties which two coupled quantum systems may not exhibit at the same time. However, as both these properties can be understood in terms of the…
In-phase synchronization is a special case of synchronous behavior when coupled oscillators have the same phases for any time moments. Such behavior appears naturally for nearly identical coupled limit-cycle oscillators when the coupling…
For a system of globally pulse-coupled phase-oscillators, we derive conditions for stability of the completely synchronous state and all possible two-cluster states and explain how the different states are naturally connected via…
We study the response of an ensemble of synchronized phase oscillators to an external harmonic perturbation applied to one of the oscillators. Our main goal is to relate the propagation of the perturbation signal to the structure of the…
We investigate synchronization effects in quantum self-sustained oscillators theoretically using the micromaser as a model system. We use the probability distribution for the relative phase as a tool for quantifying the emergence of…
A model of two self-sustained oscillators interacting through memristive coupling is studied. Memristive coupling is realized by using a cubic memristor model. Numerical simulation is combined with theoretical analysis by means of…
Effects of synchronization in a system of two coupled oscillators with time-delayed feedback are investigated. Phase space of a system with time delay is infinite-dimensional. Thus, the picture of synchronization in such systems acquires…
Two types of phase synchronization (accordingly, two scenarios of breaking phase synchronization) between coupled stochastic oscillators are shown to exist depending on the discrepancy between the control parameters of interacting…
We study ensembles of globally coupled, nonidentical phase oscillators subject to correlated noise, and we identify several important factors that cause noise and coupling to synchronize or desychronize a system. By introducing noise in…
Synchronization, which is caused by mutual coupling, and turnover, which is the replacement of old components with new ones, are observed in various open systems consisting of many components. Although these phenomena can co-occur, the…
Clock synchronization is a widely discussed topic in the engineering literature. Ensuring that individual clocks are closely aligned is important in network systems, since the correct timing of various events in a network is usually…
We study, both analytically and numerically, the dynamics of mechanical oscillators kept in motion by a feedback force, which is generated electronically from a signal produced by the oscillators themselves. This kind of self-sustained…
Synchronization is the process of achieving identical dynamics among coupled identical units. If the units are different from each other, their dynamics cannot become identical; yet, after transients, there may emerge a functional…
We introduce a system of pulse coupled oscillators that can change both their phases and frequencies; and prove that when there is a separation of time scales between phase and frequency adjustment the system converges to exact synchrony on…
Experimental study on noise-induced synchronization of crystal oscillators is presented. Two types of circuits were constructed: one consists of two Pierce oscillators that were isolated from each other and received a common noise input,…
The conditions under which synchronization is achieved for a one-dimensional ring of identical phase oscillators with Kuramoto-like local coupling are studied. The system is approached in the weakly coupled approximation as phase units.…
We propose a method for detecting the presence of synchronization of self-sustained oscillator by external driving with linearly varying frequency. The method is based on a continuous wavelet transform of the signals of self-sustained…