Synchronisation of complex networks via partial contraction principle

  • Authors:

  • Kezan Li;Weigang Sun;Xinchu Fu

  • Affiliations:

  • Department of Mathematics, Shanghai University, Shanghai, 200444, PR China.;The School of Science, Hangzhou Dianzi University, Hangzhou, 310018, PR China.;Department of Mathematics, Shanghai University, Shanghai, 200444, PR China

  • Venue:
  • International Journal of Systems, Control and Communications
  • Year:
  • 2009

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Abstract

Based on partial contraction principle, we study the complete synchronisation for approximately globally coupled networks (almost all nodes are connected). By contraction for a system, we mean that initial conditions or temporary disturbances are forgotten exponentially fast, so that all trajectories of this system converge to a unique trajectory. We identify the region of coupling strength required for achieving synchronisation for these networks without using the eigenvalues of their coupling matrices. Avoiding the computation of the eigenvalues of coupling matrix, this method becomes more effective as to studying the problem of synchronisation for that kinds of network than most other approaches. Numerical examples verify the efficiency of this method.