Synchronization

By Helmut Jürgensen. Information and Computation, 2018

609 citations recorded by the source corpus.

A BSTRACT . We study general random dynamical systems of continuous maps on some compact metric space. Assuming a local contraction condition and uniqueness of the stationary measure, we establish probabilistic limit laws such as the central limit theorem, the strong law of large numbers, and the law of the iterated logarithm. Moreover, we study exponential synchronization and synchronization on average. In the particular case of iterated function systems on S 1 , we analyze synchronization rates and describe their large deviations. In the case of C 1+ β -diffeomorphisms, these deviations on random orbits are obtained from the large deviations of the expected Lyapunov exponent.

Subfields: Artificial Intelligence

View Paper: https://www.semanticscholar.org/paper/2a36a1b187bcf478dccedd0d412c3fe89fa59f91

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

Citations in the corpus

Coherence–incoherence patterns in a ring of non-locally coupled phase oscillators (2013, background): “Examples are synchronization of neuronal oscillations in brain [1, 2, 3], entrainment in coupled Belousov-Zhabotinsky chemically reacting cells [4, 5], Josephson junction circuits [6] and mode-locked lasers [7], other references also can be found in [8].”
Strong Field Interactions between a Nanomagnet and a Photonic Cavity (2009, background): “Phase-locking of coupled oscillators [130] is a well-known phenomenon in nonlinear dynamics, i.”
The hydrodynamics of swimming microorganisms (2008, background): “In that case, in-phase locking is obtained provided that the circular trajectory of each cilium is allowed to vary in response to hydrodynamic interactions [230].”
Synchronization in complex networks (2008, background): “A nice description of experiments carried out in human beings, in which their circadian rhythms are altered, can be found in the books by Strogatz (2003b) and Pikovsky et al. (2001).”
Braess's paradox in oscillator networks, desynchronization and power outage (2012, methodology): “Content from this work may be used under the terms of the Creative Commons Attribution-NonCommercialShareAlike 3.0 licence.”
Kernel method for nonlinear granger causality. (2007, background): “The analysis of the synchronization between time series [1] is an important tool to study communications between different components of complex systems.”
Sufficient Conditions for Fast Switching Synchronization in Time-Varying Network Topologies (2005, background): “See one of the many excellent reviews now available, including [11, 50, 15, 57, 26, 42].”
Dynamic hebbian learning in adaptive frequency oscillators (2006, background): “It is well known that when the oscillator has its intrinsic frequency ω close to one frequency component of the periodic input, it will phase-lock (this phenomenon is also called entrainment) [19].”