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Indicating the synchronization bifurcation points using the early warning signals in two case studies: Continuous and explosive synchronization

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  • Karimi Rahjerdi, Bahareh
  • Ramamoorthy, Ramesh
  • Nazarimehr, Fahimeh
  • Rajagopal, Karthikeyan
  • Jafari, Sajad

Abstract

Synchronization is one of the interesting collective behaviors of oscillators. It refers to a phenomenon in which some dynamically connected systems behave the same. In dynamic systems, as the bifurcation points of the system approach, the system slows down and returns to its steady-state later with a slight disturbance. The system's slowness before bifurcation points is called critical slowing down, which can be measured using early warning (EW) indicators. This paper considers two dynamic systems: the Kuramoto model and the Rössler system. Two networks are considered to show continuous and explosive synchronization in each system. Then the synchronization bifurcation point (SBP) of each case is indicated using the EW signals calculated using the time series of synchronization measures. EW signals measure the slowness in the synchronous benchmark time series. Two EW signals, skewness and kurtosis, are applied. The results show that the SBPs in various cases and systems can be predicted using the EW signals.

Suggested Citation

  • Karimi Rahjerdi, Bahareh & Ramamoorthy, Ramesh & Nazarimehr, Fahimeh & Rajagopal, Karthikeyan & Jafari, Sajad, 2022. "Indicating the synchronization bifurcation points using the early warning signals in two case studies: Continuous and explosive synchronization," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    • Handle: RePEc:eee:chsofr:v:164:y:2022:i:c:s0960077922008359
    DOI: 10.1016/j.chaos.2022.112656
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    Cited by:

    1. Wu, Yong & Ding, Qianming & Huang, Weifang & Hu, Xueyan & Ye, Zhiqiu & Jia, Ya, 2024. "Dynamic modulation of external excitation enhance synchronization in complex neuronal network," Chaos, Solitons & Fractals, Elsevier, vol. 183(C).

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