IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v87y2016icp1-11.html
   My bibliography  Save this article

Adaptive synchronization of fractional Lorenz systems using a reduced number of control signals and parameters

Author

Listed:
  • Aguila-Camacho, Norelys
  • Duarte-Mermoud, Manuel A.
  • Delgado-Aguilera, Efredy

Abstract

This paper analyzes the synchronization of two fractional Lorenz systems in two cases: the first one considering fractional Lorenz systems with unknown parameters, and the second one considering known upper bounds on some of the fractional Lorenz systems parameters. The proposed control strategies use a reduced number of control signals and control parameters, employing mild assumptions. The stability of the synchronization errors is analytically demonstrated in all cases, and the convergence to zero of the synchronization errors is analytically proved in the case when the upper bounds on some system parameters are assumed to be known. Simulation studies are presented, which allows verifying the effectiveness of the proposed control strategies.

Suggested Citation

  • Aguila-Camacho, Norelys & Duarte-Mermoud, Manuel A. & Delgado-Aguilera, Efredy, 2016. "Adaptive synchronization of fractional Lorenz systems using a reduced number of control signals and parameters," Chaos, Solitons & Fractals, Elsevier, vol. 87(C), pages 1-11.
    • Handle: RePEc:eee:chsofr:v:87:y:2016:i:c:p:1-11
    DOI: 10.1016/j.chaos.2016.02.038
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077916300650
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2016.02.038?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. Jian Yuan & Bao Shi & Wenqiang Ji, 2013. "Adaptive Sliding Mode Control of a Novel Class of Fractional Chaotic Systems," Advances in Mathematical Physics, Hindawi, vol. 2013, pages 1-13, September.
    2. Bernd Blasius & Amit Huppert & Lewi Stone, 1999. "Complex dynamics and phase synchronization in spatially extended ecological systems," Nature, Nature, vol. 399(6734), pages 354-359, May.
    3. Wang, Yan-Wu & Guan, Zhi-Hong, 2006. "Generalized synchronization of continuous chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 27(1), pages 97-101.
    4. Ping Zhou & Xiao-You Yang, 2011. "A Novel Hybrid Function Projective Synchronization between Different Fractional-Order Chaotic Systems," Discrete Dynamics in Nature and Society, Hindawi, vol. 2011, pages 1-15, August.
    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. Wang, Cong & Zhang, Hong-li & Fan, Wen-hui, 2017. "Generalized dislocated lag function projective synchronization of fractional order chaotic systems with fully uncertain parameters," Chaos, Solitons & Fractals, Elsevier, vol. 98(C), pages 14-21.
    2. Kocamaz, Uğur Erkin & Cevher, Barış & Uyaroğlu, Yılmaz, 2017. "Control and synchronization of chaos with sliding mode control based on cubic reaching rule," Chaos, Solitons & Fractals, Elsevier, vol. 105(C), pages 92-98.

    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 & 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.
    2. Ge, Zheng-Ming & Chang, Ching-Ming & Chen, Yen-Sheng, 2006. "Anti-control of chaos of single time scale brushless dc motors and chaos synchronization of different order systems," Chaos, Solitons & Fractals, Elsevier, vol. 27(5), pages 1298-1315.
    3. Xu, Yuhua & Zhou, Wuneng & Fang, Jian-an, 2009. "Hybrid dislocated control and general hybrid projective dislocated synchronization for the modified Lü chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1305-1315.
    4. 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.
    5. Hoang, Thang Manh, 2011. "Complex synchronization manifold in coupled time-delayed systems," Chaos, Solitons & Fractals, Elsevier, vol. 44(1), pages 48-57.
    6. Singh, Piyush Pratap & Singh, Jay Prakash & Roy, B.K., 2014. "Synchronization and anti-synchronization of Lu and Bhalekar–Gejji chaotic systems using nonlinear active control," Chaos, Solitons & Fractals, Elsevier, vol. 69(C), pages 31-39.
    7. Suresh, R. & Senthilkumar, D.V. & Lakshmanan, M. & Kurths, J., 2016. "Emergence of a common generalized synchronization manifold in network motifs of structurally different time-delay systems," Chaos, Solitons & Fractals, Elsevier, vol. 93(C), pages 235-245.
    8. 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 sy," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    9. Mahmoud, Gamal M. & Aly, Shaban A. & Farghaly, Ahmed A., 2007. "On chaos synchronization of a complex two coupled dynamos system," Chaos, Solitons & Fractals, Elsevier, vol. 33(1), pages 178-187.
    10. Valenti, D. & Tranchina, L. & Brai, M. & Caruso, A. & Cosentino, C. & Spagnolo, B., 2008. "Environmental metal pollution considered as noise: Effects on the spatial distribution of benthic foraminifera in two coastal marine areas of Sicily (Southern Italy)," Ecological Modelling, Elsevier, vol. 213(3), pages 449-462.
    11. Martínez-Guerra, Rafael & Mata-Machuca, Juan L., 2014. "Generalized synchronization via the differential primitive element," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 848-857.
    12. Bahn, Volker & Krohn, William B. & O’Connor, Raymond J., 2008. "Dispersal leads to spatial autocorrelation in species distributions: A simulation model," Ecological Modelling, Elsevier, vol. 213(3), pages 285-292.
    13. Lei, Youming & Xu, Wei & Shen, Jianwei, 2007. "Robust synchronization of chaotic non-autonomous systems using adaptive-feedback control," Chaos, Solitons & Fractals, Elsevier, vol. 31(2), pages 371-379.
    14. Karnatak, Rajat & Ramaswamy, Ram & Feudel, Ulrike, 2014. "Conjugate coupling in ecosystems: Cross-predation stabilizes food webs," Chaos, Solitons & Fractals, Elsevier, vol. 68(C), pages 48-57.
    15. Goldwyn, Eli E. & Hastings, Alan, 2008. "When can dispersal synchronize populations?," Theoretical Population Biology, Elsevier, vol. 73(3), pages 395-402.
    16. Michal Fečkan & T. Sathiyaraj & JinRong Wang, 2020. "Synchronization of Butterfly Fractional Order Chaotic System," Mathematics, MDPI, vol. 8(3), pages 1-12, March.
    17. Kuetche Mbe, E.S. & Fotsin, H.B. & Kengne, J. & Woafo, P., 2014. "Parameters estimation based adaptive Generalized Projective Synchronization (GPS) of chaotic Chua’s circuit with application to chaos communication by parametric modulation," Chaos, Solitons & Fractals, Elsevier, vol. 61(C), pages 27-37.
    18. Alexander Korotkov & Sergei Petrovskii, 2023. "Extinctions in a Metapopulation with Nonlinear Dispersal Coupling," Mathematics, MDPI, vol. 11(20), pages 1-22, October.
    19. Agiza, H.N. & Matouk, A.E., 2006. "Adaptive synchronization of Chua’s circuits with fully unknown parameters," Chaos, Solitons & Fractals, Elsevier, vol. 28(1), pages 219-227.
    20. Li, Guo-Hui, 2009. "Generalized synchronization of chaos based on suitable separation," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2056-2062.

    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:87:y:2016:i:c:p:1-11. 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.