IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v95y2017icp33-41.html
   My bibliography  Save this article

Chaos in a low dimensional fractional order nonautonomous nonlinear oscillator

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077916303599
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2016.12.007?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Mishra, Shalabh Kumar & Upadhyay, Dharmendra Kumar & Gupta, Maneesha, 2018. "An approach to improve the performance of fractional-order sinusoidal oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 126-135.
    2. Waseem, Waseem & Sulaiman, M. & Aljohani, Abdulah Jeza, 2020. "Investigation of fractional models of damping material by a neuroevolutionary approach," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    3. Guo, Yingjia, 2017. "Stochastic regime switching SIR model driven by Lévy noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 479(C), pages 1-11.
    4. Jimin Yu & Zeming Zhao & Yabin Shao, 2023. "On Cauchy Problems of Caputo Fractional Differential Inclusion with an Application to Fractional Non-Smooth Systems," Mathematics, MDPI, vol. 11(3), pages 1-18, January.
    5. Liu, Xinzhi & Stechlinski, Peter, 2016. "Hybrid stabilization and synchronization of nonlinear systems with unbounded delays," Applied Mathematics and Computation, Elsevier, vol. 280(C), pages 140-161.
    6. Pang, Denghao & Jiang, Wei & Liu, Song & Jun, Du, 2019. "Stability analysis for a single degree of freedom fractional oscillator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 498-506.
    7. Chiou, Juing-Shian & Cheng, Chun-Ming, 2009. "Stabilization analysis of the switched discrete-time systems using Lyapunov stability theorem and genetic algorithm," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 751-759.
    8. C. Sánchez-López & V. H. Carbajal-Gómez & M. A. Carrasco-Aguilar & I. Carro-Pérez, 2018. "Fractional-Order Memristor Emulator Circuits," Complexity, Hindawi, vol. 2018, pages 1-10, May.
    9. Abir Lassoued & Olfa Boubaker, 2017. "Dynamic Analysis and Circuit Design of a Novel Hyperchaotic System with Fractional-Order Terms," Complexity, Hindawi, vol. 2017, pages 1-10, October.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:95:y:2017:i:c:p:33-41. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.