Detection of synchronization from univariate data using wavelet transform

A method is proposed for detecting from univariate data the presence of synchronization of a self-sustained oscillator by external driving with varying frequency. The method is based on the analysis of difference between the oscillator instantaneous phases calculated using continuous wavelet transform at time moments shifted by a certain constant value relative to each other. We apply our method to a driven asymmetric van der Pol oscillator, experimental data from a driven electronic oscillator with delayed feedback and human heartbeat time series. In the latest case, the analysis of the heart rate variability data reveals synchronous regimes between the respiration and slow oscillations in blood pressure.Comment: 10 pages, 9 figure

Dispersal and noise: Various modes of synchrony in\ud ecological oscillators

We use the theory of noise-induced phase synchronization to analyze the effects of dispersal on the synchronization of a pair of predator-prey systems within a fluctuating environment (Moran effect). Assuming that each isolated local population acts as a limit cycle oscillator in the deterministic limit, we use phase reduction and averaging methods to derive a Fokker–Planck equation describing the evolution of the probability density for pairwise phase differences between the oscillators. In the case of common environmental noise, the oscillators ultimately synchronize. However the approach to synchrony depends on whether or not dispersal in the absence of noise supports any stable asynchronous states. We also show how the combination of correlated (shared) and uncorrelated (unshared) noise with dispersal can lead to a multistable\ud steady-state probability density

Synchronization transitions in ensembles of noisy oscillators with bi-harmonic coupling

We describe synchronization transitions in an ensemble of globally coupled phase oscillators with a bi-harmonic coupling function, and two sources of disorder - diversity of intrinsic oscillatory frequencies and external independent noise. Based on the self-consistent formulation, we derive analytic solutions for different synchronous states. We report on various non-trivial transitions from incoherence to synchrony where possible scenarios include: simple supercritical transition (similar to classical Kuramoto model), subcritical transition with large area of bistability of incoherent and synchronous solutions, and also appearance of symmetric two-cluster solution which can coexist with regular synchronous state. Remarkably, we show that the interplay between relatively small white noise and finite-size fluctuations can lead to metastable asynchronous solution

Dynamical Systems on Networks: A Tutorial

We give a tutorial for the study of dynamical systems on networks. We focus especially on "simple" situations that are tractable analytically, because they can be very insightful and provide useful springboards for the study of more complicated scenarios. We briefly motivate why examining dynamical systems on networks is interesting and important, and we then give several fascinating examples and discuss some theoretical results. We also briefly discuss dynamical systems on dynamical (i.e., time-dependent) networks, overview software implementations, and give an outlook on the field.Comment: 39 pages, 1 figure, submitted, more examples and discussion than original version, some reorganization and also more pointers to interesting direction

Ergogenic and psychological effects of synchronous music during circuit-type exercise

This is the post print version of the article. The official published version can be obtained from the link below.Objectives: Motivational music when synchronized with movement has been found to improve performance in anaerobic and aerobic endurance tasks, although gender differences pertaining to the potential benefits of such music have seldom been investigated. The present study addresses the psychological and ergogenic effects of synchronous music during circuit-type exercise. Design: A mixed-model design was employed in which there was a within-subjects factor (two experimental conditions and a control) and a between-subjects factor (gender). Methods: Participants (N ¼ 26) performed six circuit-type exercises under each of three synchronous conditions: motivational music, motivationally-neutral (oudeterous) music, and a metronome control. Dependent measures comprised anaerobic endurance, which was assessed using the number of repetitions performed prior to the failure to maintain synchronicity, and post-task affect, which was assessed using Hardy and Rejeski’s (1989) Feeling Scale. Mixed-model 3 (Condition) X 2 (Gender) ANOVAs, ANCOVAs, and MANOVA were used to analyze the data. Results: Synchronous music did not elicit significant (p < .05) ergogenic or psychological effects in isolation; rather, significant (p < .05) Condition X Gender interaction effects emerged for both total repetitions and mean affect scores. Women and men showed differential affective responses to synchronous music and men responded more positively than women to metronomic regulation of their movements. Women derived the greatest overall benefit from both music conditions. Conclusions: Men may place greater emphasis on the metronomic regulation of movement than the remaining, extra-rhythmical, musical qualities. Men and women appear to exhibit differential responses in terms of affective responses to synchronous music