Transition of synchronization of coupled maps in modular networks

Bin Zhang, Ru-Hai Du, Sheng-Jun Wang and Shi-Xian Qu
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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

International Journal of Modern Physics C (IJMPC), 2020, vol. 31, issue 01, 1-12

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.

Keywords: Modular network; modularity; phase synchronization; synchronization transition (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1142/S0129183120500114

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