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Oscillator networks display intricate synchronization patterns. Determining their stability typically requires incorporating the symmetries of the network coupling. Going beyond analyses that appeal only to a network's automorphism group,…

Dynamical Systems · Mathematics 2020-12-14 J. Emenheiser , A. Salova , J. Snyder , J. P. Crutchfield , R. M. D'Souza

Cluster synchronization is a fundamental phenomenon in systems of coupled oscillators. Here, we investigate clustering patterns that emerge in a unidirectional ring of four delay-coupled electrochemical oscillators. A voltage parameter in…

Dynamical Systems · Mathematics 2023-06-28 Andrew Keane , Alannah Neff , Karen Blaha , Andreas Amann , Philipp Hövel

We study the effect of common noise on coupled active rotators. While such a noise always facilitates synchrony, coupling may be attractive or repulsing. We develop an analytical approach based on a transformation to approximate…

Statistical Mechanics · Physics 2017-12-21 Anastasiya V. Dolmatova , Denis S. Goldobin , Arkady Pikovsky

Two oscillators coupled to a two-level system which in turn is coupled to an infinite number of oscillators (reservoir) are considered, bringing to light the occurrence of synchronization. A detailed analysis clarifies the physical…

Quantum Physics · Physics 2017-09-13 B. Militello , H. Nakazato , A. Napoli

We consider the Kuramoto-Sakaguchi model of identical coupled phase oscillators with a common noisy forcing. While common noise always tends to synchronize the oscillators, a strong repulsive coupling prevents the fully synchronous state…

Statistical Mechanics · Physics 2019-04-12 Chen Chris Gong , Chunming Zheng , Ralf Toenjes , Arkady Pikovsky

Using methods of numerical simulation, we analyze the influence of L\'evy noise on synchronization of excitable oscillators in the regime of coherence resonance. Three cases are under consideration: forced synchronization of a single…

Adaptation and Self-Organizing Systems · Physics 2025-05-05 Ivan A. Korneev , Vladimir V. Semenov

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…

Statistical Mechanics · Physics 2020-04-22 Alessandro Campa

Synchronization phenomena, frequency shift and phase noise are often limiting key factors in the performances of oscillators. The perturbation projection method allows to characterize how the oscillator's output is modified by these…

Signal Processing · Electrical Eng. & Systems 2019-05-14 Michele Bonnin , Fernando Corinto , Marco Gilli

This paper addresses the amplitude and phase dynamics of a large system non-linear coupled, non-identical damped harmonic oscillators, which is based on recent research in coupled oscillation in optomechanics. Our goal is to investigate the…

Chaotic Dynamics · Physics 2015-06-23 P. Cudmore , C. A. Holmes

Coupled distinct arrays of nonlinear oscillators have been shown to have a regime of high frequency, or ultra-harmonic, oscillations that are at multiples of the natural frequency of individual oscillators. The coupled array architectures…

Pattern Formation and Solitons · Physics 2007-05-23 Alexandra S. Landsman , Ira B. Schwartz

We present a detailed analysis of a model for the synchronization of nonlinear oscillators due to reactive coupling and nonlinear frequency pulling. We study the model for the mean field case of all-to-all coupling, deriving results for the…

Adaptation and Self-Organizing Systems · Physics 2009-11-11 M. C. Cross , J. L. Rogers , Ron Lifshitz , A. Zumdieck

Motivated from a wide range of applications, various methods to control synchronization in coupled oscillators have been proposed. Previous studies have demonstrated that global feedback typically induces three macroscopic behaviors:…

Adaptation and Self-Organizing Systems · Physics 2021-07-07 Ayumi Ozawa , Hiroshi Kori

Noise in entangled quantum systems is difficult to characterize due to many-body effects involving multiple degrees of freedom. This noise poses a challenge to quantum computing, where two-qubit gate performance is critical. Here, we…

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…

The phenomenon of delay-induced resonance implies that in a nonlinear system a time-delay term may be used as an effective enhancer of the oscillations caused by an external forcing maintaining the same frequency. This is possible for the…

Chaotic Dynamics · Physics 2020-04-22 Julia Cantisán , Mattia Coccolo , Jesús M. Seoane , Miguel A. F. Sanjuán

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…

Mathematical Physics · Physics 2012-11-06 J. Borresen , D. Broomhead

Synchronization is an omnipresent collective phenomenon in nature and technology, whose understanding is in particular for real-world systems still elusive. We study the synchronization transition in a phase oscillator system with two…

Adaptation and Self-Organizing Systems · Physics 2023-08-02 Rico Berner , Annie Lu , Igor M. Sokolov

Synchronization and chaos are two well known and ubiquitous phenomena in nature. Interestingly, under specific conditions, coupled chaotic systems can display synchronization in some of their observables. Here, we experimentally investigate…

Chaotic Dynamics · Physics 2021-09-01 Guilhem Madiot , Franck Correia , Sylvain Barbay , Rémy Braive

We study synchronization of oscillators that are indirectly coupled through their interaction with an environment. We give criteria for the stability or instability of a synchronized oscillation. Using these criteria we investigate…

Adaptation and Self-Organizing Systems · Physics 2009-11-13 Guy Katriel

We report the observation of a novel and non-trivial synchronization state in a system consisting of three oscillators coupled in a linear chain. For certain ranges of coupling strength the weakly coupled oscillator pair exhibits phase…