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Golden mean relevance for chaos inhibition in a system of two coupled modified van der Pol oscillators

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  • Stan, Cristina
  • Cristescu, C.P.
  • Agop, M.

Abstract

In this work, we present a novel evidence of the importance of the golden mean criticality of a system of oscillators in agreement with El Naschie’s E-infinity theory. We focus on chaos inhibition in a system of two coupled modified van der Pol oscillators. Depending on the coupling between the two oscillators, the system shows chaotic behavior for different ranges of the coupling parameter. Chaos suppression, as a transition from irregular behavior to a periodical one, is induced by perturbing the system with a harmonic signal with amplitude considerably lower than the value which causes entrainment. The frequency of the perturbation is related to the main frequencies in the spectrum of the freely running system (without perturbation) by the golden mean. We demonstrate that this effect is also obtained for a perturbation with frequency such that the ratio of half the frequency of the first main component in the freely running chaotic spectrum over the frequency of the perturbation is very close (five digits coincidence) to the golden mean. This result is shown to hold for arbitrary values of the coupling parameter in the various ranges of chaotic dynamics of the free running system.

Suggested Citation

  • Stan, Cristina & Cristescu, C.P. & Agop, M., 2007. "Golden mean relevance for chaos inhibition in a system of two coupled modified van der Pol oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 31(4), pages 1035-1040.
    • Handle: RePEc:eee:chsofr:v:31:y:2007:i:4:p:1035-1040
    DOI: 10.1016/j.chaos.2006.04.056
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    References listed on IDEAS

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    1. Bin, Deng & Jiang, Wang & Xiangyang, Fei, 2006. "Synchronizing two coupled chaotic neurons in external electrical stimulation using backstepping control," Chaos, Solitons & Fractals, Elsevier, vol. 29(1), pages 182-189.
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    Cited by:

    1. Stan, Cristina & Cristescu, C.P. & Alexandroaei, D. & Agop, M., 2009. "Stochastic resonance and vibrational resonance in an excitable system: The golden mean barrier," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 727-734.
    2. Cristescu, C.P. & Mereu, B. & Stan, Cristina & Agop, M., 2009. "Feigenbaum scenario in the dynamics of a metal–oxide semiconductor heterostructure under harmonic perturbation. Golden mean criticality," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 975-980.

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