IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v35y2008i4p705-717.html
   My bibliography  Save this article

Chaos synchronization of fractional order modified duffing systems with parameters excited by a chaotic signal

Author

Listed:
  • Ge, Zheng-Ming
  • Ou, Chan-Yi

Abstract

In this paper, chaos synchronizations of two uncoupled fractional order chaotic modified Duffing systems are obtained. By replacing their corresponding parameters by the same function of chaotic state variables of a third chaotic system, chaos synchronization can be obtained. The method is named parameter excited chaos synchronization which can be successfully obtained for very low total fractional order 0.2. Numerical simulations are illustrated by phase portrait, Poincaré map and state error plots.

Suggested Citation

  • Ge, Zheng-Ming & Ou, Chan-Yi, 2008. "Chaos synchronization of fractional order modified duffing systems with parameters excited by a chaotic signal," Chaos, Solitons & Fractals, Elsevier, vol. 35(4), pages 705-717.
    • Handle: RePEc:eee:chsofr:v:35:y:2008:i:4:p:705-717
    DOI: 10.1016/j.chaos.2006.05.101
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S096007790600484X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2006.05.101?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. Chen, Hsien-Keng, 2005. "Synchronization of two different chaotic systems: a new system and each of the dynamical systems Lorenz, Chen and Lü," Chaos, Solitons & Fractals, Elsevier, vol. 25(5), pages 1049-1056.
    2. Lu, Jun Guo, 2005. "Chaotic dynamics and synchronization of fractional-order Arneodo’s systems," Chaos, Solitons & Fractals, Elsevier, vol. 26(4), pages 1125-1133.
    3. Ge, Z.-M. & Cheng, J.-W., 2005. "Chaos synchronization and parameter identification of three time scales brushless DC motor system," Chaos, Solitons & Fractals, Elsevier, vol. 24(2), pages 597-616.
    4. 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.
    5. Chen, Hsien-Keng, 2005. "Global chaos synchronization of new chaotic systems via nonlinear control," Chaos, Solitons & Fractals, Elsevier, vol. 23(4), pages 1245-1251.
    6. Ge, Zheng-Ming & Lee, Ching-I, 2005. "Control, anticontrol and synchronization of chaos for an autonomous rotational machine system with time-delay," Chaos, Solitons & Fractals, Elsevier, vol. 23(5), pages 1855-1864.
    7. Ge, Zheng-Ming & Chen, Yen-Sheng, 2005. "Adaptive synchronization of unidirectional and mutual coupled chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 881-888.
    8. He, G.L. & Zhou, S.P., 2005. "What is the exact condition for fractional integrals and derivatives of Besicovitch functions to have exact box dimension?," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 867-879.
    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. Nazim I Mahmudov & Sameer Bawaneh & Areen Al-Khateeb, 2019. "On a Coupled System of Fractional Differential Equations with Four Point Integral Boundary Conditions," Mathematics, MDPI, vol. 7(3), pages 1-14, March.
    2. Ahmad, Bashir & Ntouyas, Sotiris K. & Alsaedi, Ahmed, 2016. "On a coupled system of fractional differential equations with coupled nonlocal and integral boundary conditions," Chaos, Solitons & Fractals, Elsevier, vol. 83(C), pages 234-241.
    3. Wang, Jieyang & Mou, Jun & Xiong, Li & Zhang, Yingqian & Cao, Yinghong, 2021. "Fractional-order design of a novel non-autonomous laser chaotic system with compound nonlinearity and its circuit realization," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    4. Ahmad, Bashir & Luca, Rodica, 2018. "Existence of solutions for sequential fractional integro-differential equations and inclusions with nonlocal boundary conditions," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 516-534.
    5. Agarwal, Ravi P. & Ahmad, Bashir & Garout, Doa’a & Alsaedi, Ahmed, 2017. "Existence results for coupled nonlinear fractional differential equations equipped with nonlocal coupled flux and multi-point boundary conditions," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 149-161.
    6. Muthaiah Subramanian & Jehad Alzabut & Mohamed I. Abbas & Chatthai Thaiprayoon & Weerawat Sudsutad, 2022. "Existence of Solutions for Coupled Higher-Order Fractional Integro-Differential Equations with Nonlocal Integral and Multi-Point Boundary Conditions Depending on Lower-Order Fractional Derivatives and," Mathematics, MDPI, vol. 10(11), pages 1-19, May.
    7. Fathy, Mohamed & Abdelgaber, K.M., 2022. "Approximate solutions for the fractional order quadratic Riccati and Bagley-Torvik differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    8. Hallaji, Majid & Dideban, Abbas & Khanesar, Mojtaba Ahmadieh & kamyad, Ali vahidyan, 2018. "Optimal synchronization of non-smooth fractional order chaotic systems with uncertainty based on extension of a numerical approach in fractional optimal control problems," Chaos, Solitons & Fractals, Elsevier, vol. 115(C), pages 325-340.

    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. Ge, Zheng-Ming & Chang, Ching-Ming, 2009. "Nonlinear generalized synchronization of chaotic systems by pure error dynamics and elaborate nondiagonal Lyapunov function," Chaos, Solitons & Fractals, Elsevier, vol. 39(4), pages 1959-1974.
    3. Ge, Zheng-Ming & Hsu, Mao-Yuan, 2008. "Chaos excited chaos synchronizations of integral and fractional order generalized van der Pol systems," Chaos, Solitons & Fractals, Elsevier, vol. 36(3), pages 592-604.
    4. Tam, Lap Mou & Si Tou, Wai Meng, 2008. "Parametric study of the fractional-order Chen–Lee system," Chaos, Solitons & Fractals, Elsevier, vol. 37(3), pages 817-826.
    5. Chen, Juhn-Horng & Chen, Hsien-Keng & Lin, Yu-Kai, 2009. "Synchronization and anti-synchronization coexist in Chen–Lee chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 39(2), pages 707-716.
    6. Ge, Zheng-Ming & Ou, Chan-Yi, 2007. "Chaos in a fractional order modified Duffing system," Chaos, Solitons & Fractals, Elsevier, vol. 34(2), pages 262-291.
    7. Ge, Zheng-Ming & Lin, Guo-Hua, 2007. "The complete, lag and anticipated synchronization of a BLDCM chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 34(3), pages 740-764.
    8. Chen, Juhn-Horng, 2008. "Controlling chaos and chaotification in the Chen–Lee system by multiple time delays," Chaos, Solitons & Fractals, Elsevier, vol. 36(4), pages 843-852.
    9. Ge, Zheng-Ming & Hsu, Mao-Yuan, 2007. "Chaos in a generalized van der Pol system and in its fractional order system," Chaos, Solitons & Fractals, Elsevier, vol. 33(5), pages 1711-1745.
    10. Ge, Zheng-Ming & Jhuang, Wei-Ren, 2007. "Chaos, control and synchronization of a fractional order rotational mechanical system with a centrifugal governor," Chaos, Solitons & Fractals, Elsevier, vol. 33(1), pages 270-289.
    11. Ge, Zheng-Ming & Zhang, An-Ray, 2007. "Chaos in a modified van der Pol system and in its fractional order systems," Chaos, Solitons & Fractals, Elsevier, vol. 32(5), pages 1791-1822.
    12. Petráš, Ivo, 2008. "A note on the fractional-order Chua’s system," Chaos, Solitons & Fractals, Elsevier, vol. 38(1), pages 140-147.
    13. 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.
    14. Wang, Zheng & Chau, K.T., 2008. "Anti-control of chaos of a permanent magnet DC motor system for vibratory compactors," Chaos, Solitons & Fractals, Elsevier, vol. 36(3), pages 694-708.
    15. Deshpande, Amey S. & Daftardar-Gejji, Varsha, 2017. "On disappearance of chaos in fractional systems," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 119-126.
    16. Lu, Jun Guo, 2006. "Synchronization of a class of fractional-order chaotic systems via a scalar transmitted signal," Chaos, Solitons & Fractals, Elsevier, vol. 27(2), pages 519-525.
    17. 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.
    18. Tam, Lap Mou & Chen, Juhn Horng & Chen, Hsien Keng & Si Tou, Wai Meng, 2008. "Generation of hyperchaos from the Chen–Lee system via sinusoidal perturbation," Chaos, Solitons & Fractals, Elsevier, vol. 38(3), pages 826-839.
    19. Tang, Yinggan & Guan, Xinping, 2009. "Parameter estimation of chaotic system with time-delay: A differential evolution approach," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 3132-3139.
    20. Hammami, S. & Ben Saad, K. & Benrejeb, M., 2009. "On the synchronization of identical and non-identical 4-D chaotic systems using arrow form matrix," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 101-112.

    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:35:y:2008:i:4:p:705-717. 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.