Discovering, Constructing, and Analyzing Synchronous Clusters of Oscillators in a Complex Network Using Symmetries

  • Louis M. Pecora
  • Francesco Sorrentino
  • Aaron M. Hagerstrom
  • Thomas E. Murphy
  • Rajarshi Roy
Chapter
Part of the Nonlinear Systems and Complexity book series (NSCH, volume 20)

Abstract

Synchronization is a collective phenomenon that appears in many natural and man-made networks of oscillators or dynamical systems such as telecommunication, neuronal and biological networks. An interesting form of synchronization is cluster synchronization where the network becomes partitioned into groups of oscillator nodes which synchronize to each other, but not to other nodes in other groups or clusters. We present a technique and develop methods for the analysis of network dynamics that shows the connection between network symmetries and cluster formation. We also experimentally confirm these approaches in the context of real networks with heterogeneities and noise using an electro-optic network. We find an interesting scenario for the appearance of chimera synchronization in these cases of identical cluster synchronization. We also extend these methods to networks which have Laplacian coupling and show that we can analyze cases where there are synchronization clusters which do not directly arise from symmetries, but can be built from clusters found by a symmetry analysis.

Keywords

Synchronization Networks Chaos Chimera Symmetry 

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Louis M. Pecora
    • 1
  • Francesco Sorrentino
    • 2
  • Aaron M. Hagerstrom
    • 3
    • 4
  • Thomas E. Murphy
    • 5
    • 6
  • Rajarshi Roy
    • 3
    • 4
    • 7
  1. 1.U. S. Naval Research LaboratoryWashingtonUSA
  2. 2.Department of Mechanical EngineeringUniversity of New MexicoAlbuquerqueUSA
  3. 3.Department of PhysicsUniversity of MarylandCollege ParkUSA
  4. 4.Institute for Research in Electronics and Applied PhysicsUniversity of MarylandCollege ParkUSA
  5. 5.Department of Electrical and Computer EngineeringUniversity of MarylandCollege ParkUSA
  6. 6.Institute for Research in Electronics and Applied PhysicsUniversity of MarylandCollege ParkUSA
  7. 7.Institute for Physical Science and TechnologyUniversity of MarylandCollege ParkUSA

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