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Optimal synchronization of circulant and non-circulant oscillators

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Listed:
  • Panahi, Shirin
  • Nazarimehr, Fahimeh
  • Jafari, Sajad
  • Sprott, Julien C.
  • Perc, Matjaž
  • Repnik, Robert

Abstract

We study the synchronization of coupled identical circulant and non-circulant oscillators using single variable and different multi-variable coupling schemes. We use the master stability function to determine conditions for synchronization, in particular the necessary coupling parameter that ensures a stable synchronization manifold. We show that for circulant oscillators, the smallest coupling parameter for synchronization is needed when multi-variable coupling with the same coupling coefficients is applied. Conversely, for non-circulant oscillators, no such general conclusions are attainable in that the smallest coupling parameter cannot be attributed to a particular coupling setup.

Suggested Citation

  • Panahi, Shirin & Nazarimehr, Fahimeh & Jafari, Sajad & Sprott, Julien C. & Perc, Matjaž & Repnik, Robert, 2021. "Optimal synchronization of circulant and non-circulant oscillators," Applied Mathematics and Computation, Elsevier, vol. 394(C).
    • Handle: RePEc:eee:apmaco:v:394:y:2021:i:c:s0096300320307839
    DOI: 10.1016/j.amc.2020.125830
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    References listed on IDEAS

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    1. Mostaghimi, Soudeh & Nazarimehr, Fahimeh & Jafari, Sajad & Ma, Jun, 2019. "Chemical and electrical synapse-modulated dynamical properties of coupled neurons under magnetic flow," Applied Mathematics and Computation, Elsevier, vol. 348(C), pages 42-56.
    2. Peng, Dong & Sun, Kehui & He, Shaobo & Alamodi, Abdulaziz O.A., 2019. "What is the lowest order of the fractional-order chaotic systems to behave chaotically?," Chaos, Solitons & Fractals, Elsevier, vol. 119(C), pages 163-170.
    3. Nazarimehr, Fahimeh & Panahi, Shirin & Jalili, Mahdi & Perc, Matjaž & Jafari, Sajad & Ferčec, Brigita, 2020. "Multivariable coupling and synchronization in complex networks," Applied Mathematics and Computation, Elsevier, vol. 372(C).
    4. Andrzej Stefanski & Tomasz kapitaniak, 2000. "Using chaos synchronization to estimate the largest lyapunov exponent of nonsmooth systems," Discrete Dynamics in Nature and Society, Hindawi, vol. 4, pages 1-9, January.
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    Cited by:

    1. Zandi-Mehran, Nazanin & Nazarimehr, Fahimeh & Rajagopal, Karthikeyan & Ghosh, Dibakar & Jafari, Sajad & Chen, Guanrong, 2022. "FFT bifurcation: A tool for spectrum analyzing of dynamical systems," Applied Mathematics and Computation, Elsevier, vol. 422(C).

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