Synchronization transitions caused by time-varying coupling functions. (16th December 2019)

• Record Type: Journal Article
• Authors: Hagos, Zeray; Stankovski, Tomislav; Newman, Julian; Pereira, Tiago; McClintock, Peter V. E.; Stefanovska, Aneta
• Is Part Of: Philosophical transactions. Volume 377:Number 2160(2019)
• Publication Date: 2019-12-16
• Subjects: coupling functions -- coupled oscillators -- interactions -- dynamical systems; Physical sciences -- Periodicals; Engineering -- Periodicals; Mathematics -- Periodicals; 500
• DOI: 10.1098/rsta.2019.0275
• Languages: English
• ISSNs: 1364-503X

Abstract

Abstract : Interacting dynamical systems are widespread in nature. The influence that one such system exerts on another is described by a coupling function; and the coupling functions extracted from the time-series of interacting dynamical systems are often found to be time-varying. Although much effort has been devoted to the analysis of coupling functions, the influence of time-variability on the associated dynamics remains largely unexplored. Motivated especially by coupling functions in biology, including the cardiorespiratory and neural delta-alpha coupling functions, this paper offers a contribution to the understanding of effects due to time-varying interactions. Through both numerics and mathematically rigorous theoretical consideration, we show that for time-variable coupling functions with time-independent net coupling strength, transitions into and out of phase- synchronization can occur, even though the frozen coupling functions determine phase-synchronization solely by virtue of their net coupling strength. Thus the information about interactions provided by the shape of coupling functions plays a greater role in determining behaviour when these coupling functions are time-variable. This article is part of the theme issue 'Coupling functions: dynamical interaction mechanisms in the physical, biological and social sciences'.