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Chaos in a low dimensional fractional order nonautonomous nonlinear oscillator

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  • Palanivel, J.
  • Suresh, K.
  • Sabarathinam, S.
  • Thamilmaran, K.

Abstract

We report the dynamics of a low dimensional fractional order forced LCR circuit using Chua’s diode. The stability analysis is performed for each segment of the piecewise linear curve of Chua’s diode and the conditions for the oscillation and double scroll chaos are obtained. The effect of fractional order on the bifurcation points are studied with the help of bifurcation diagrams. We consider both the derivatives of the systems current and voltage as fractional derivatives. When the order of the derivatives is decreased, the system exhibits interesting dynamical behavior. For instance, the value of the fractional order corresponding to the voltage is decreased, the chaotic regime in the system decreases. But in the case of current, the chaotic regime in the system increases initially and beyond a certain value of order, the chaotic regime decreases and extinguishes from the system. We found the lowest order for exhibiting chaos in the fractional order of the circuit as 2.1. For the first time, the experimental analogue of our proposed system is made by using the frequency domain approximation. The results are obtained from the experimental observations are compared with numerical simulations and found that they match closely with each other. The existence of chaos in the circuit is analyzed with the help of 0-1 test and power spectrum.

Suggested Citation

  • Palanivel, J. & Suresh, K. & Sabarathinam, S. & Thamilmaran, K., 2017. "Chaos in a low dimensional fractional order nonautonomous nonlinear oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 95(C), pages 33-41.
    • Handle: RePEc:eee:chsofr:v:95:y:2017:i:c:p:33-41
    DOI: 10.1016/j.chaos.2016.12.007
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    References listed on IDEAS

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    1. Srinivasan, K. & Chandrasekar, V.K. & Venkatesan, A. & Raja Mohamed, I., 2016. "Duffing–van der Pol oscillator type dynamics in Murali–Lakshmanan–Chua (MLC) circuit," Chaos, Solitons & Fractals, Elsevier, vol. 82(C), pages 60-71.
    2. Li, Ping & Zhong, Shou-Ming & Cui, Jin-Zhong, 2009. "Stability analysis of linear switching systems with time delays," Chaos, Solitons & Fractals, Elsevier, vol. 40(1), pages 474-480.
    3. Radwan, A.G. & Soliman, A.M. & Elwakil, A.S. & Sedeek, A., 2009. "On the stability of linear systems with fractional-order elements," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2317-2328.
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    Cited by:

    1. Kamal, F.M. & Elsonbaty, A. & Elsaid, A., 2021. "A novel fractional nonautonomous chaotic circuit model and its application to image encryption," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    2. Vaibhav Varshney & S. Leo Kingston & Sabarathinam Srinivasan & Suresh Kumarasamy, 2024. "Hidden attractors in fractional-order discrete maps," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 97(10), pages 1-10, October.
    3. Palanivel, J. & Suresh, K. & Premraj, D. & Thamilmaran, K., 2018. "Effect of fractional-order, time-delay and noisy parameter on slow-passage phenomenon in a nonlinear oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 106(C), pages 35-43.

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