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Synchronization transitions caused by time-varying coupling functions.

Zeray Hagos1,2, Tomislav Stankovski3,4, Julian Newman4

  • 1Institute of Mathematical and Computer Sciences, University of São Paulo, São Carlos 13566-590, Brazil.

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|October 29, 2019
PubMed
Summary

Time-varying coupling functions in dynamical systems can cause phase-synchronization transitions, even with constant net coupling strength. The shape of these functions significantly influences system behavior when interactions change over time.

Keywords:
coupled oscillatorscoupling functionsdynamical systemsinteractions

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Area of Science:

  • Dynamical Systems Theory
  • Complex Systems Science
  • Nonlinear Dynamics

Background:

  • Interacting dynamical systems are prevalent in natural phenomena.
  • Coupling functions describe system interactions, often exhibiting time-variability.
  • The impact of time-varying coupling on system dynamics is under-explored.

Purpose of the Study:

  • To investigate the effects of time-varying coupling functions on the dynamics of interacting systems.
  • To understand how time-variability influences phase-synchronization.
  • To explore biological coupling functions, such as cardiorespiratory and neural delta-alpha coupling.

Main Methods:

  • Numerical simulations of interacting dynamical systems.
  • Mathematically rigorous theoretical analysis.
  • Examination of time-varying coupling functions with time-independent net coupling strength.

Main Results:

  • Phase-synchronization transitions (into and out of sync) can occur with time-variable coupling.
  • These transitions happen despite constant net coupling strength.
  • The shape of the coupling function becomes crucial for determining system behavior when it varies over time.

Conclusions:

  • Time-variability in coupling functions introduces complex dynamics not predicted by static analysis.
  • The detailed structure of coupling functions, not just their average strength, significantly impacts system behavior.
  • Findings have implications for understanding biological interactions and other complex systems.