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Optimum topology and coupling strength for synchronization

Author

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  • Xi, Xiaojian
  • Panahi, Shirin
  • Pham, Viet-Thanh
  • Wang, Zhen
  • Jafari, Sajad
  • Hussain, Iqtadar

Abstract

The category of the small-world networks is neither random (like random networks) nor highly ordered (like regular networks). Their special properties are the combination of high clustering coefficient and short path length which can be seen in many real world networks. Synchronization of a small-world topology of dynamical network receives a great deal of attention in recent years. Here, the synchronization of a small-world network is compared with a regular and random network with the same number of nodes and links. To this end, identical network contains 100 nodes with three different topologies (regular, small-world and random) are considered. The linear stability of the synchronization manifold of these networks is investigated by the help of master stability function approach. Therefore, the synchronization problem is linked to the Laplacian matrix of the network. Through numerical analysis, we show that the optimum coupling strength belongs to the small-world network with proper rewiring probabilities.

Suggested Citation

  • Xi, Xiaojian & Panahi, Shirin & Pham, Viet-Thanh & Wang, Zhen & Jafari, Sajad & Hussain, Iqtadar, 2020. "Optimum topology and coupling strength for synchronization," Applied Mathematics and Computation, Elsevier, vol. 379(C).
    • Handle: RePEc:eee:apmaco:v:379:y:2020:i:c:s0096300320301958
    DOI: 10.1016/j.amc.2020.125226
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    References listed on IDEAS

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    1. M. E. J. Newman & D. J. Watts, 1999. "Renormalization Group Analysis of the Small-World Network Model," Working Papers 99-04-029, Santa Fe Institute.
    2. Dror Kenett & Shlomo Havlin, 2015. "Network science: a useful tool in economics and finance," Mind & Society: Cognitive Studies in Economics and Social Sciences, Springer;Fondazione Rosselli, vol. 14(2), pages 155-167, November.
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