Synchronous oscillations in networks of time-delay coupled inert systems

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Abstract

We discuss the emergence of oscillations in networks of inert single-input-singleoutput systems which interact via linear, time-delay coupling functions. We present conditions for 1. the solutions of the time-delay coupled systems to be bounded, 2. the network equilibrium to be unique, and 3. the network equilibrium to be unstable. If these conditions are all satisfied the network of time-delay coupled inert systems has a non-trivial oscillatory solution. In addition, we show that a necessary and sufficient condition for the emerge of oscillations in such networks is that the considered systems are at least second order. Moreover, using recent results on the existence of partial synchronization manifolds, we identify the patterns of oscillation that may emerge.

Original languageEnglish
Pages (from-to)31-36
Number of pages6
JournalIFAC-PapersOnLine
Volume48
Issue number18
DOIs
Publication statusPublished - 1 Nov 2015
Event4th IFAC Conference on Analysis and Control of Chaotic Systems (IFAC CHAOS 2015) - Tokyo, Japan
Duration: 26 Aug 201528 Aug 2015
Conference number: 4
http://ctrl.mech.se.tmu.ac.jp/chaos2015/
http://ctrl.mech.se.tmu.ac.jp/chaos2015/

Keywords

  • Coupling
  • Instability
  • Networks
  • Oscillation
  • Synchronization
  • Time-delay

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