Testing for phase synchronization

TL;DR: The cluster-phase method of Frank and Richardson (2010) was used to analyze movement data from the rocking chair movements of six-member groups who rocked their chairs while seated in a circle facing the center, and the group level synchrony measure was able to distinguish between situations where synchrony would have been possible and situations where it would be impossible.

TL;DR: In this article, a quantitative approach to detect phase synchronization in noisy experimental multivariate data is discussed, and a test statistic based on the Kuramoto order parameter is derived for rejecting the null hypothesis of zero phase synchronization at given significance levels.

TL;DR: The findings indicate that the unweighted and weighted phase lag index are less prone to the influence of common sources but that this advantage may lead to constrictions limiting the applicability of these methods.

TL;DR: The definitions of instantaneous phase, the indexes of phase synchronization and their significance test, the issues that may affect the detection of phase synchronized signals, and the extensions ofphase synchronization analysis are discussed.

TL;DR: Weak Convergence in Metric Spaces as discussed by the authors is one of the most common modes of convergence in metric spaces, and it can be seen as a form of weak convergence in metric space.

TL;DR: This chapter describes the linking of two chaotic systems with a common signal or signals and highlights that when the signs of the Lyapunov exponents for the subsystems are all negative the systems are synchronized.

TL;DR: This work discusseschronization of complex dynamics by external forces, which involves synchronization of self-sustained oscillators and their phase, and its applications in oscillatory media and complex systems.

TL;DR: In this paper, the convergence of distributions is considered in the context of conditional probability, i.e., random variables and expected values, and the probability of a given distribution converging to a certain value.