Synchronization transitions caused by time-varying coupling functions

Hagos, Zeray and Stankovski, Tomislav and Newman, Julian and Pereira, Tiago and McClintock, Peter V. E. and Stefanovska, Aneta (2019) Synchronization transitions caused by time-varying coupling functions. Philosophical Transactions of the Royal Society of London A, 377 (2160): 20190275. ISSN 0264-3820

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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.