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Original Articles

Complete synchronisation of linear oscillator networks

Pages 800-814 | Received 13 Jul 2011, Accepted 11 Feb 2012, Published online: 14 Mar 2012

References

  • Berman , A and Plemmons , RJ . 1979 . Nonnegative Matrices in the Mathematical Sciences , New York : Academic Press .
  • Bilharz , H . 1944 . Bemerkungen zu einem Satze von Hurwitz . Zeitschrift für Angewandte Mathematik , 24 : 77 – 82 .
  • Chopra , N and Spong , MW . 2005 . On Synchronization of Kuramoto Oscillators . IEEE Conference on Decision and Control and European Control Conference . 2005 . pp. 3916 – 3922 .
  • Gantmacher , FR . 1986 . Matrizentheorie Berlin: Deutscher Verlag der Wissenschaften
  • Jadbabaie , A , Lin , J and Morse , AS . 2003 . Coordination of Groups of Mobile Autonomous Agents using Nearest Neighbour Rules . IEEE Transactions on Automatic Control , 48 : 988 – 1001 .
  • Jadbabaie , A , Motee , N and Barahona , M . 2004 . On the Stability of the Kuramoto Model of Coupled Nonlinear Oscillators . American Control Conference . 2004 . pp. 4296 – 4301 .
  • Kuramoto , Y . 1975 . Self-entrainment of a Population of Coupled Non-linear Oscillators . in International Symposium on Mathematical Problems in Theoretical Physics , : 420 – 422 .
  • Kuramoto , Y . 1984 . Chemical Oscillations, Waves, and Turbulence , Berlin : Springer-Verlag .
  • Lunze , J . 2011a . Synchronisable Nodes in Networked Systems . Journal of Physics A: Mathematics and Theoretical , 44 : 045103
  • Lunze , J . 2011b . An Internal-model Principle for the Synchronisation of Autonomous Agents with Individual Dynamics . IEEE Conference on Decision and Control, Orlando . 2011b . pp. 2106 – 2111 .
  • Olfati-Saber , R and Murray , RM . 2004 . Consensus Problems in Networks of Agents with Switching Topology and Time-delays . IEEE Transactions on Automatic Control , 49 : 1520 – 1533 .
  • Osipov , G , Kurths , J and Zhou , C . 2007 . Synchronization in Oscillatory Networks , Berlin : Springer-Verlag .
  • Pecora , LM and Carroll , TL . 1998 . Master Stability Functions for Synchronized Coupled Systems . Physical Review Letters , 80 : 2109 – 2112 .
  • Pikovsky , A , Rosenblum , M and Kurths , J . 2001 . Synchronization. A Universal Concept in Nonlinear Sciences , Cambridge : Cambridge University Press .
  • Ren , W , Beard , RW and Atkin , EA . 2007 . Information Consensus in Multivehicle Cooperative Control . IEEE Control Systems Magazine , : 71 – 82 .
  • Ren , W and Cao , Y . 2011 . Distributed Coordination of Multi-Agent Networks , London : Springer-Verlag .
  • Sakaguchi , H , Shinomoto , S and Kuramoto , Y . 1987 . Local and Global Self-entrainments in Oscillator Lattices . Progress in Theoretical Physics , 77 : 1005 – 1010 .
  • Scardovi , L and Sepulchre , R . 2009 . Synchronization in Networks of Identical Linear Systems . Automatica , 45 : 2557 – 2562 .
  • Strogatz , SH . 2000 . From Kuramoto to Crawford: Exploring the Onset of Synchronization in Populations of Coupled Oscillators . Physica, D , 143 : 1 – 20 .
  • Wieland , P , Sepulchre , R and Allgöwer , F . 2011 . An Internal Model Principle Is Necessary and Sufficient for Linear Output Synchronization . Automatica , 47 : 1068 – 1074 .
  • Wu , CW and Chua , LO . 1995 . Synchronization in an Array of Linearly Coupled Dynamical Systems . IEEE Transactions on Circuits and Systems, Part I , 42 : 430 – 447 .

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