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Explosive synchronization dependence on initial conditions: The minimal Kuramoto model

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  • Bayani, Atiyeh
  • Jafari, Sajad
  • Azarnoush, Hamed
  • Nazarimehr, Fahimeh
  • Boccaletti, Stefano
  • Perc, Matjaž

Abstract

Transitions from incoherent to coherent dynamical states can be observed in various real-world networks, ranging from neurons to power-grids. These transitions can be explosive or continuous, with far-reaching implications for the functioning of the affected system. It is therefore of the utmost importance to determine the conditions under which such transitions occur. While a lot of studies in literature focused on the dynamical and/or structural network properties that may generate explosive synchronization, here we report on the effects of different initial conditions. To this purpose, we consider the minimal network of Kuramoto oscillator that may display explosive synchronization, and we show that the nature of the transition changes from continuous to discontinuous as phases are differently initialized. We also determine the critical coupling strength for explosive synchronization, which also depends on the initial conditions.

Suggested Citation

  • Bayani, Atiyeh & Jafari, Sajad & Azarnoush, Hamed & Nazarimehr, Fahimeh & Boccaletti, Stefano & Perc, Matjaž, 2023. "Explosive synchronization dependence on initial conditions: The minimal Kuramoto model," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    • Handle: RePEc:eee:chsofr:v:169:y:2023:i:c:s0960077923001443
    DOI: 10.1016/j.chaos.2023.113243
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    1. Li, Kexin & Bao, Bocheng & Ma, Jun & Chen, Mo & Bao, Han, 2022. "Synchronization transitions in a discrete memristor-coupled bi-neuron model," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
    2. Dai, Xiangfeng & Li, Xuelong & Gutiérrez, Ricardo & Guo, Hao & Jia, Danyang & Perc, Matjaž & Manshour, Pouya & Wang, Zhen & Boccaletti, Stefano, 2020. "Explosive synchronization in populations of cooperative and competitive oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    3. G. Filatrella & A. H. Nielsen & N. F. Pedersen, 2008. "Analysis of a power grid using a Kuramoto-like model," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 61(4), pages 485-491, February.
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    9. Bayani, Atiyeh & Alexander, Prasina & Azarnoush, Hamed & Rajagopal, Karthikeyan & Jafari, Sajad & Nazarimehr, Fahimeh, 2023. "Designing networks with specific synchronization transitions independent of the system’s dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 632(P1).
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