IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v44y2011i10p845-850.html
   My bibliography  Save this article

Generation of multi-wing chaotic attractor in fractional order system

Author

Listed:
  • Zhang, Chaoxia
  • Yu, Simin

Abstract

In this paper, a novel approach is proposed for generating multi-wing chaotic attractors from the fractional linear differential system via nonlinear state feedback controller equipped with a duality-symmetric multi-segment quadratic function. The main idea is to design a proper nonlinear state feedback controller by using four construction criterions from a fundamental fractional differential nominal linear system, so that the controlled fractional differential system can generate multi-wing chaotic attractors. It is the first time in the literature to report the multi-wing chaotic attractors from an uncoupled fractional differential system. Furthermore, some basic dynamical analysis and numerical simulations are also given, confirming the effectiveness of the proposed method.

Suggested Citation

  • Zhang, Chaoxia & Yu, Simin, 2011. "Generation of multi-wing chaotic attractor in fractional order system," Chaos, Solitons & Fractals, Elsevier, vol. 44(10), pages 845-850.
    • Handle: RePEc:eee:chsofr:v:44:y:2011:i:10:p:845-850
    DOI: 10.1016/j.chaos.2011.06.017
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077911001238
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2011.06.017?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. Lu, Jun Guo & Chen, Guanrong, 2006. "A note on the fractional-order Chen system," Chaos, Solitons & Fractals, Elsevier, vol. 27(3), pages 685-688.
    2. Li, Chunguang & Chen, Guanrong, 2004. "Chaos and hyperchaos in the fractional-order Rössler equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 341(C), pages 55-61.
    3. Yu, Simin & Tang, Wallace K.S., 2009. "Generation of n×m-scroll attractors in a two-port RCL network with hysteresis circuits," Chaos, Solitons & Fractals, Elsevier, vol. 39(2), pages 821-830.
    4. Ahmad, Wajdi M., 2005. "Generation and control of multi-scroll chaotic attractors in fractional order systems," Chaos, Solitons & Fractals, Elsevier, vol. 25(3), pages 727-735.
    5. Bouallegue, Kais & Chaari, Abdessattar & Toumi, Ahmed, 2011. "Multi-scroll and multi-wing chaotic attractor generated with Julia process fractal," Chaos, Solitons & Fractals, Elsevier, vol. 44(1), pages 79-85.
    6. Laskin, N. & Zaslavsky, G., 2006. "Nonlinear fractional dynamics on a lattice with long range interactions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 368(1), pages 38-54.
    7. Ahmad, Wajdi M., 2006. "A simple multi-scroll hyperchaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 27(5), pages 1213-1219.
    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. Das, Saptarshi & Pan, Indranil & Das, Shantanu, 2016. "Effect of random parameter switching on commensurate fractional order chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 157-173.
    2. Cui, Li & Lu, Ming & Ou, Qingli & Duan, Hao & Luo, Wenhui, 2020. "Analysis and Circuit Implementation of Fractional Order Multi-wing Hidden Attractors," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).

    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. Ge, Zheng-Ming & Yi, Chang-Xian, 2007. "Chaos in a nonlinear damped Mathieu system, in a nano resonator system and in its fractional order systems," Chaos, Solitons & Fractals, Elsevier, vol. 32(1), pages 42-61.
    2. Soliman, Nancy S. & Tolba, Mohammed F. & Said, Lobna A. & Madian, Ahmed H. & Radwan, Ahmed G., 2019. "Fractional X-shape controllable multi-scroll attractor with parameter effect and FPGA automatic design tool software," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 292-307.
    3. Aguirre-Hernández, B. & Campos-Cantón, E. & López-Renteria, J.A. & Díaz González, E.C., 2015. "A polynomial approach for generating a monoparametric family of chaotic attractors via switched linear systems," Chaos, Solitons & Fractals, Elsevier, vol. 71(C), pages 100-106.
    4. Yalçin, Müştak E., 2007. "Multi-scroll and hypercube attractors from a general jerk circuit using Josephson junctions," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1659-1666.
    5. 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).
    6. Petráš, Ivo, 2008. "A note on the fractional-order Chua’s system," Chaos, Solitons & Fractals, Elsevier, vol. 38(1), pages 140-147.
    7. Deepika, Deepika & Kaur, Sandeep & Narayan, Shiv, 2018. "Uncertainty and disturbance estimator based robust synchronization for a class of uncertain fractional chaotic system via fractional order sliding mode control," Chaos, Solitons & Fractals, Elsevier, vol. 115(C), pages 196-203.
    8. Huang, Xiuqi & Wang, Xiangjun, 2021. "Regularity of fractional stochastic convolution and its application to fractional stochastic chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 149(C).
    9. Khanzadeh, Alireza & Pourgholi, Mahdi, 2016. "Robust Synchronization of Fractional-Order Chaotic Systems at a Pre-Specified Time Using Sliding Mode Controller with Time-Varying Switching Surfaces," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 69-77.
    10. Grassi, Giuseppe & Severance, Frank L. & Miller, Damon A., 2009. "Multi-wing hyperchaotic attractors from coupled Lorenz systems," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 284-291.
    11. Azam, Anam & Aqeel, Muhammad & Sunny, Danish Ali, 2022. "Generation of Multidirectional Mirror Symmetric Multiscroll Chaotic Attractors (MSMCA) in Double Wing Satellite Chaotic System," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    12. Tavazoei, Mohammad Saleh & Haeri, Mohammad, 2008. "Synchronization of chaotic fractional-order systems via active sliding mode controller," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(1), pages 57-70.
    13. Munoz-Pacheco, J.M. & Zambrano-Serrano, E. & Volos, Ch. & Tacha, O.I. & Stouboulos, I.N. & Pham, V.-T., 2018. "A fractional order chaotic system with a 3D grid of variable attractors," Chaos, Solitons & Fractals, Elsevier, vol. 113(C), pages 69-78.
    14. Yu, Simin & Tang, Wallace K.S., 2009. "Tetrapterous butterfly attractors in modified Lorenz systems," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1740-1749.
    15. Sharma, Vivek & Shukla, Manoj & Sharma, B.B., 2018. "Unknown input observer design for a class of fractional order nonlinear systems," Chaos, Solitons & Fractals, Elsevier, vol. 115(C), pages 96-107.
    16. Zhang, Weiwei & Zhou, Shangbo & Li, Hua & Zhu, Hao, 2009. "Chaos in a fractional-order Rössler system," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1684-1691.
    17. Mahmoud, Emad E. & Higazy, M. & Alotaibi, Hammad & Abo-Dahab, S.M. & Abdel-Khalek, S. & Khalil, E.M., 2021. "Quaternion anti-synchronization of a novel realizable fractional chaotic model," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    18. Chen, Liping & Pan, Wei & Wu, Ranchao & Wang, Kunpeng & He, Yigang, 2016. "Generation and circuit implementation of fractional-order multi-scroll attractors," Chaos, Solitons & Fractals, Elsevier, vol. 85(C), pages 22-31.
    19. Cheng, Guanghui & Li, Dan & Yao, Yuangen & Gui, Rong, 2023. "Multi-scroll chaotic attractors with multi-wing via oscillatory potential wells," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    20. Dlamini, A. & Doungmo Goufo, E.F., 2023. "Generation of self-similarity in a chaotic system of attractors with many scrolls and their circuit’s implementation," Chaos, Solitons & Fractals, Elsevier, vol. 176(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:eee:chsofr:v:44:y:2011:i:10:p:845-850. 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.