Synchronisation of Weakly Coupled Oscillators

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Abstract

The synchronization phenomenon was reported for the first time by Christiaan Huygens, when he noticed the strange tendency of a couple of clocks to synchronise their movements. More recently this phenomena was shown to be ubiquitous in nature and it is broadly studied by its applications, for example in biological cycles. We consider the problem of synchronization of a general network of linearly coupled oscillators, not necessarily identical. In this case the existence of a linear synchronization space is not expected, so we present an approach based on the proof of the existence of a synchronization manifold, the so-called generalised synchronization. Based on some results developed by R. Smith and on Wazewski’s principle, a general theory on the existence of invariant manifolds that attract the solutions of the system that are bounded in the future, is presented. Applications and estimates on parameters for the existence of synchronization are presented for several examples: systems of coupled pendulum type equations, coupled Lorenz systems of equations, and oscillators coupled through a medium, among many others.

Original languageEnglish
Title of host publicationModeling, Dynamics, Optimization and Bioeconomics IV - DGS VI JOLATE and ICABR, Selected Contributions
EditorsAlberto Pinto, David Zilberman
PublisherSpringer
Pages323-354
Number of pages32
ISBN (Electronic)978-3-030-78163-7
ISBN (Print)978-3-030-78162-0
DOIs
Publication statusPublished - 2021
Event6th International Conference on Dynamics Games and Science, DGS-VI-2018, 19th Latin American Conference on Economic Theory, JOLATE 2018 and 21st International Consortium on Applied Bioeconomy Research, ICABR 2017 - Berkeley, United States
Duration: 30 May 20172 Jun 2017

Publication series

NameSpringer Proceedings in Mathematics and Statistics
PublisherSpringer
Volume365
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

Conference

Conference6th International Conference on Dynamics Games and Science, DGS-VI-2018, 19th Latin American Conference on Economic Theory, JOLATE 2018 and 21st International Consortium on Applied Bioeconomy Research, ICABR 2017
Country/TerritoryUnited States
CityBerkeley
Period30/05/172/06/17

Keywords

  • Coupled oscillators
  • Dissipative systems
  • Invariant manifolds
  • Synchronisation

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