Home > Research > Publications & Outputs > Synchronisation transitions caused by time-vary...

Electronic data

  • ReRevised_coupling_paper

    Accepted author manuscript, 3 MB, PDF document

    Available under license: CC BY: Creative Commons Attribution 4.0 International License

View graph of relations

Synchronisation transitions caused by time-varying coupling functions

Research output: Contribution to journalJournal article

Forthcoming
<mark>Journal publication date</mark>9/09/2019
<mark>Journal</mark>Philosophical Transactions of the Royal Society of London A
Publication statusAccepted/In press
Original languageEnglish

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-synchronisation can occur, even though the frozen coupling functions determine phase-synchronisation 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.