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Analysis of fractional order Bonhoeffer–van der Pol oscillator

Author

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  • Gafiychuk, V.
  • Datsko, B.
  • Meleshko, V.

Abstract

We investigate a Bonhoeffer–van der Pol dynamical system with fractional derivatives of different orders. Spectral analysis is fulfilled analytically for certain relationships between derivative orders and numerically for any relation between them. It is shown that such a system could be more unstable than the system with integer derivatives even for fractional order indices less than one. Different types of oscillations appear as a result of this instability. Computer simulation of the typical oscillations demonstrating the observed effects are performed.

Suggested Citation

  • Gafiychuk, V. & Datsko, B. & Meleshko, V., 2008. "Analysis of fractional order Bonhoeffer–van der Pol oscillator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(2), pages 418-424.
    • Handle: RePEc:eee:phsmap:v:387:y:2008:i:2:p:418-424
    DOI: 10.1016/j.physa.2007.09.006
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    References listed on IDEAS

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    1. Gafiychuk, V.V. & Datsko, B.Yo., 2006. "Pattern formation in a fractional reaction–diffusion system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 365(2), pages 300-306.
    2. Ge, Zheng-Ming & Ou, Chan-Yi, 2007. "Chaos in a fractional order modified Duffing system," Chaos, Solitons & Fractals, Elsevier, vol. 34(2), pages 262-291.
    3. Ahmed, E. & Elgazzar, A.S., 2007. "On fractional order differential equations model for nonlocal epidemics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 379(2), pages 607-614.
    4. Stanislavsky, Aleksander A., 2005. "Twist of fractional oscillations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 354(C), pages 101-110.
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    Cited by:

    1. Zambrano-Serrano, Ernesto & Bekiros, Stelios & Platas-Garza, Miguel A. & Posadas-Castillo, Cornelio & Agarwal, Praveen & Jahanshahi, Hadi & Aly, Ayman A., 2021. "On chaos and projective synchronization of a fractional difference map with no equilibria using a fuzzy-based state feedback control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 578(C).
    2. Xiao, Min & Zheng, Wei Xing & Cao, Jinde, 2013. "Approximate expressions of a fractional order Van der Pol oscillator by the residue harmonic balance method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 89(C), pages 1-12.

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