IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v150y2021ics0960077921004264.html
   My bibliography  Save this article

Estimating the ultimate bounds and synchronization of fractional-order plasma chaotic systems

Author

Listed:
  • Peng, Qiu
  • Jian, Jigui

Abstract

This paper focuses on the Mittag–Leffler ultimate bounds (MLUBs) and synchronization of fractional-order plasma chaotic systems (FOPCSs). For one thing, by choosing some appropriate generalized Lyapunov functions and combining fractional-order differential inequalities, some new estimates on the 3D ellipsoid and cylindrical domains as well as a rotatory paraboloid of the bounds for the FOPCS are acquired according to system parameters, which perfect the previous studies and may infer a few new estimates. For another, linear feedback control tactics with two inputs or one input as well as fractional-order adaptive control with one input and a single variable are presented to realize the synchronization of two FOPCSs. Several new sufficient conditions for synchronization are analytically obtained by using inequality methods. The boundaries and feedback gain constants are easier to be calculated and the controller structures are simpler. Finally, numerical simulations are shown to confirm the correctness of the presented synchronization schemes.

Suggested Citation

  • Peng, Qiu & Jian, Jigui, 2021. "Estimating the ultimate bounds and synchronization of fractional-order plasma chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    • Handle: RePEc:eee:chsofr:v:150:y:2021:i:c:s0960077921004264
    DOI: 10.1016/j.chaos.2021.111072
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077921004264
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2021.111072?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, Jigui & Wan, Peng, 2015. "Global exponential convergence of generalized chaotic systems with multiple time-varying and finite distributed delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 431(C), pages 152-165.
    2. Laskin, Nick, 2000. "Fractional market dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 287(3), pages 482-492.
    3. Huang, Chengdai & Cao, Jinde, 2017. "Active control strategy for synchronization and anti-synchronization of a fractional chaotic financial system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 473(C), pages 262-275.
    4. Jian, Jigui & Wu, Kai & Wang, Baoxian, 2020. "Global Mittag-Leffler boundedness and synchronization for fractional-order chaotic systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    5. Hajipour, Ahamad & Hajipour, Mojtaba & Baleanu, Dumitru, 2018. "On the adaptive sliding mode controller for a hyperchaotic fractional-order financial system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 497(C), pages 139-153.
    6. Chee, Chin Yi & Xu, Daolin, 2005. "Secure digital communication using controlled projective synchronisation of chaos," Chaos, Solitons & Fractals, Elsevier, vol. 23(3), pages 1063-1070.
    7. Gong, Xiao-Li & Liu, Xi-Hua & Xiong, Xiong, 2019. "Chaotic analysis and adaptive synchronization for a class of fractional order financial system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 522(C), pages 33-42.
    8. Yang, Yingjuan & Qi, Guoyuan, 2018. "Mechanical analysis and bound of plasma chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 108(C), pages 187-195.
    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. Liu, Ping & Zhang, Yulan & Mohammed, Khidhair Jasim & Lopes, António M. & Saberi-Nik, Hassan, 2023. "The global dynamics of a new fractional-order chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 175(P2).
    2. Hou, Yi-You & Lin, Ming-Hung & Saberi-Nik, Hassan & Arya, Yogendra, 2024. "Boundary analysis and energy feedback control of fractional-order extended Malkus–Robbins dynamo system," Chaos, Solitons & Fractals, Elsevier, vol. 183(C).
    3. Ren, Lei & Lin, Ming-Hung & Abdulwahab, Abdulkareem & Ma, Jun & Saberi-Nik, Hassan, 2023. "Global dynamical analysis of the integer and fractional 4D hyperchaotic Rabinovich system," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    4. Yang, Jin & Jian, Jigui, 2023. "Quasi-invariant and attracting sets of competitive neural networks with time-varying and infinite distributed delays," Chaos, Solitons & Fractals, Elsevier, vol. 177(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. Jian, Jigui & Wu, Kai & Wang, Baoxian, 2020. "Global Mittag-Leffler boundedness and synchronization for fractional-order chaotic systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    2. Qijia Yao & Hadi Jahanshahi & Larissa M. Batrancea & Naif D. Alotaibi & Mircea-Iosif Rus, 2022. "Fixed-Time Output-Constrained Synchronization of Unknown Chaotic Financial Systems Using Neural Learning," Mathematics, MDPI, vol. 10(19), pages 1-14, October.
    3. Wang, Fei & Yang, Yongqing, 2018. "Intermittent synchronization of fractional order coupled nonlinear systems based on a new differential inequality," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 142-152.
    4. Gong, Xiao-Li & Liu, Xi-Hua & Xiong, Xiong, 2019. "Chaotic analysis and adaptive synchronization for a class of fractional order financial system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 522(C), pages 33-42.
    5. Song Xu & Hui Lv & Heng Liu & Aijing Liu, 2019. "Robust Control of Disturbed Fractional-Order Economical Chaotic Systems with Uncertain Parameters," Complexity, Hindawi, vol. 2019, pages 1-13, October.
    6. Fang, Qingxiang & Peng, Jigen, 2018. "Synchronization of fractional-order linear complex networks with directed coupling topology," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 542-553.
    7. Vasily E. Tarasov, 2019. "On History of Mathematical Economics: Application of Fractional Calculus," Mathematics, MDPI, vol. 7(6), pages 1-28, June.
    8. Peng, Qiu & Jian, Jigui, 2023. "Synchronization analysis of fractional-order inertial-type neural networks with time delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 62-77.
    9. Yi Chen & Jing Dong & Hao Ni, 2021. "ɛ-Strong Simulation of Fractional Brownian Motion and Related Stochastic Differential Equations," Mathematics of Operations Research, INFORMS, vol. 46(2), pages 559-594, May.
    10. 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.
    11. Pratap, A. & Raja, R. & Cao, J. & Lim, C.P. & Bagdasar, O., 2019. "Stability and pinning synchronization analysis of fractional order delayed Cohen–Grossberg neural networks with discontinuous activations," Applied Mathematics and Computation, Elsevier, vol. 359(C), pages 241-260.
    12. 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.
    13. G. Fern'andez-Anaya & L. A. Quezada-T'ellez & B. Nu~nez-Zavala & D. Brun-Battistini, 2019. "Katugampola Generalized Conformal Derivative Approach to Inada Conditions and Solow-Swan Economic Growth Model," Papers 1907.00130, arXiv.org.
    14. Lu, Jun Guo & Chen, Guanrong, 2006. "A note on the fractional-order Chen system," Chaos, Solitons & Fractals, Elsevier, vol. 27(3), pages 685-688.
    15. Sheu, Long-Jye & Chen, Hsien-Keng & Chen, Juhn-Horng & Tam, Lap-Mou & Chen, Wen-Chin & Lin, Kuang-Tai & Kang, Yuan, 2008. "Chaos in the Newton–Leipnik system with fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 36(1), pages 98-103.
    16. Wang, Aijuan & Liao, Xiaofeng & Dong, Tao, 2018. "Finite-time event-triggered synchronization for reaction–diffusion complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 111-120.
    17. Laskin, Nick, 2018. "Valuing options in shot noise market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 502(C), pages 518-533.
    18. Ali Balcı, Mehmet, 2017. "Time fractional capital-induced labor migration model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 477(C), pages 91-98.
    19. Majee, Suvankar & Jana, Soovoojeet & Das, Dhiraj Kumar & Kar, T.K., 2022. "Global dynamics of a fractional-order HFMD model incorporating optimal treatment and stochastic stability," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    20. Chu, Yu-Ming & Bekiros, Stelios & Zambrano-Serrano, Ernesto & Orozco-López, Onofre & Lahmiri, Salim & Jahanshahi, Hadi & Aly, Ayman A., 2021. "Artificial macro-economics: A chaotic discrete-time fractional-order laboratory model," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).

    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:150:y:2021:i:c:s0960077921004264. 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.