IDEAS home Printed from https://ideas.repec.org/a/wly/jnlaaa/v2015y2015i1n413540.html

Integer and Fractional General T‐System and Its Application to Control Chaos and Synchronization

Author

Listed:
  • Mihaela Neamţu
  • Anamaria Liţoiu
  • Petru C. Strain

Abstract

We propose a three‐dimensional autonomous nonlinear system, called the general T system, which has potential applications in secure communications and the electronic circuit. For the general T system with delayed feedback, regarding the delay as bifurcation parameter, we investigate the effect of the time delay on its dynamics. We determine conditions for the existence of the Hopf bifurcations and analyze their direction and stability. Also, the fractional order general T‐system is proposed and analyzed. We provide some numerical simulations, where the chaos attractor and the dynamics of the Lyapunov coefficients are taken into consideration. The effectiveness of the chaotic control and synchronization on schemes for the new fractional order chaotic system are verified by numerical simulations.

Suggested Citation

  • Mihaela Neamţu & Anamaria Liţoiu & Petru C. Strain, 2015. "Integer and Fractional General T‐System and Its Application to Control Chaos and Synchronization," Abstract and Applied Analysis, John Wiley & Sons, vol. 2015(1).
    • Handle: RePEc:wly:jnlaaa:v:2015:y:2015:i:1:n:413540
    DOI: 10.1155/2015/413540
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2015/413540
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2015/413540?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
    ---><---

    References listed on IDEAS

    as
    1. Tigan, Gheorghe & Opriş, Dumitru, 2008. "Analysis of a 3D chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 36(5), pages 1315-1319.
    2. Cuimei Jiang & Shutang Liu & Chao Luo, 2014. "A New Fractional-Order Chaotic Complex System and Its Antisynchronization," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-12, October.
    3. Cuimei Jiang & Shutang Liu & Chao Luo, 2014. "A New Fractional‐Order Chaotic Complex System and Its Antisynchronization," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    4. Sachin Bhalekar, 2012. "Chaos Control and Synchronization in Fractional-Order Lorenz-Like System," International Journal of Differential Equations, Hindawi, vol. 2012, pages 1-16, August.
    Full references (including those not matched with items on IDEAS)

    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. Laarem, Guessas, 2021. "A new 4-D hyper chaotic system generated from the 3-D Rösslor chaotic system, dynamical analysis, chaos stabilization via an optimized linear feedback control, it’s fractional order model and chaos synchronization using optimized fractional order sli," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    2. Yadav, Vijay K. & Shukla, Vijay K. & Das, Subir, 2021. "Exponential synchronization of fractional-order complex chaotic systems and its application," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    3. Tigan, Gheorghe & Constantinescu, Dana, 2009. "Heteroclinic orbits in the T and the Lü systems," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 20-23.
    4. Mahmoudabadi, Parvin & Tavakoli-Kakhki, Mahsan, 2021. "Tracking control with disturbance rejection of nonlinear fractional order fuzzy systems: Modified repetitive control approach," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    5. Loong Soon Tee & Zabidin Salleh, 2013. "Dynamical Analysis of a Modified Lorenz System," Journal of Mathematics, Hindawi, vol. 2013, pages 1-8, December.
    6. Assali, El Abed, 2021. "Predefined-time synchronization of chaotic systems with different dimensions and applications," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    7. Li, Xian-Feng & Chu, Yan-Dong & Zhang, Jian-Gang & Chang, Ying-Xiang, 2009. "Nonlinear dynamics and circuit implementation for a new Lorenz-like attractor," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2360-2370.
    8. Yang, Shuangling & Qu, Jingjia, 2021. "On first integrals of a family of generalized Lorenz-like systems," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    9. Wu, Yue & Zhou, Xiaobing & Chen, Jia & Hui, Bei, 2009. "Chaos synchronization of a new 3D chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1812-1819.
    10. Wu, Ranchao & Fang, Tianbao, 2015. "Stability and Hopf bifurcation of a Lorenz-like system," Applied Mathematics and Computation, Elsevier, vol. 262(C), pages 335-343.
    11. Li, Xian-Feng & Chu, Yan-Dong & Leung, Andrew Y.T. & Zhang, Hui, 2017. "Synchronization of uncertain chaotic systems via complete-adaptive-impulsive controls," Chaos, Solitons & Fractals, Elsevier, vol. 100(C), pages 24-30.
    12. Leonov, G.A. & Kuznetsov, N.V., 2015. "On differences and similarities in the analysis of Lorenz, Chen, and Lu systems," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 334-343.
    13. Vignesh, D. & He, Shaobo & Banerjee, Santo, 2023. "Modelling discrete time fractional Rucklidge system with complex state variables and its synchronization," Applied Mathematics and Computation, Elsevier, vol. 455(C).

    More about this item

    Statistics

    Access and download statistics

    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:wly:jnlaaa:v:2015:y:2015:i:1:n:413540. 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: Wiley Content Delivery (email available below). General contact details of provider: https://onlinelibrary.wiley.com/journal/4058 .

    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.