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Transition of synchronization of coupled maps in modular networks

Author

Listed:
  • Bin Zhang

    (School of Physics and Information Technology, Shaanxi Normal University, Xi’an 710119, P. R. China†Computer College, Weinan Normal University, Weinan 714099, P. R. China)

  • Ru-Hai Du

    (School of Physics and Information Technology, Shaanxi Normal University, Xi’an 710119, P. R. China)

  • Sheng-Jun Wang

    (School of Physics and Information Technology, Shaanxi Normal University, Xi’an 710119, P. R. China)

  • Shi-Xian Qu

    (School of Physics and Information Technology, Shaanxi Normal University, Xi’an 710119, P. R. China)

Abstract

Spatiotemporal patterns in the transition of phase synchronization in modular networks of coupled logistic maps are studied. The phase diagram of spatiotemporal patterns is presented by analyzing both the collective behavior of direction-phase and the changes of links connecting clusters of different phases. The spatiotemporal chaos is obtained when the coupling strength is weak. We show that the spatiotemporal chaos can be composed by clusters in periodic states. The region of periodic behaviors is independent of modularity. Then with decreasing coupling or increasing modularity, the system presents the same transition path from complete synchronization to cluster synchronization, except the network is close to fully connected networks. There are two distinctive scenarios from disordered behavior to an ordered state when the modularity ratio varies from one to zero. First, for networks with small modularity, the number of phase synchronized clusters decreases with the increasing of the coupling strength. Second, for networks with large modularity, the number of phase-synchronized clusters nonmonotonically changes with the coupling strength.

Suggested Citation

  • Bin Zhang & Ru-Hai Du & Sheng-Jun Wang & Shi-Xian Qu, 2020. "Transition of synchronization of coupled maps in modular networks," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 31(01), pages 1-12, January.
    • Handle: RePEc:wsi:ijmpcx:v:31:y:2020:i:01:n:s0129183120500114
    DOI: 10.1142/S0129183120500114
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