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Adaptive fuzzy impulsive synchronization of chaotic systems with random parameters

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  • Zhang, Xingpeng
  • Li, Dong
  • Zhang, Xiaohong

Abstract

Randomness is a common phenomenon in nonlinear systems. And conditions to reach synchronization are more complex and difficult when chaotic systems have random parameters. So in this paper, an adaptive scheme for synchronization of chaotic system with random parameters by using the fuzzy impulsive method and combining the properties of Wiener process and Ito differential is investigated. The main concepts of this paper are applying fuzzy method to approximate the nonlinear part of system, then using Ito differential to study the Wiener process of random parameters of chaotic system, and realizing synchronization under fuzzy impulsive method. The stability is analyzed by Lyapunov stability theorem. At the end of the paper, numerical simulation is presented to illustrate the effectiveness of the results obtained in this paper.

Suggested Citation

  • Zhang, Xingpeng & Li, Dong & Zhang, Xiaohong, 2017. "Adaptive fuzzy impulsive synchronization of chaotic systems with random parameters," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 77-83.
    • Handle: RePEc:eee:chsofr:v:104:y:2017:i:c:p:77-83
    DOI: 10.1016/j.chaos.2017.08.006
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    References listed on IDEAS

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    1. Salarieh, Hassan & Alasty, Aria, 2008. "Adaptive control of chaotic systems with stochastic time varying unknown parameters," Chaos, Solitons & Fractals, Elsevier, vol. 38(1), pages 168-177.
    2. Salarieh, Hassan & Shahrokhi, Mohammad, 2008. "Adaptive synchronization of two different chaotic systems with time varying unknown parameters," Chaos, Solitons & Fractals, Elsevier, vol. 37(1), pages 125-136.
    3. Wu, Cunli & Fang, Tong & Rong, Haiwu, 2007. "Chaos synchronization of two stochastic Duffing oscillators by feedback control," Chaos, Solitons & Fractals, Elsevier, vol. 32(3), pages 1201-1207.
    4. Ghamati, Mina & Balochian, Saeed, 2015. "Design of adaptive sliding mode control for synchronization Genesio–Tesi chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 75(C), pages 111-117.
    5. Feki, Moez, 2009. "Sliding mode control and synchronization of chaotic systems with parametric uncertainties," Chaos, Solitons & Fractals, Elsevier, vol. 41(3), pages 1390-1400.
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    Cited by:

    1. Wang, Lingyu & Huang, Tingwen & Xiao, Qiang, 2018. "Global exponential synchronization of nonautonomous recurrent neural networks with time delays on time scales," Applied Mathematics and Computation, Elsevier, vol. 328(C), pages 263-275.
    2. Wang, Yuangan & Yu, Honglin, 2018. "Fuzzy synchronization of chaotic systems via intermittent control," Chaos, Solitons & Fractals, Elsevier, vol. 106(C), pages 154-160.
    3. Ding, Dong & Tang, Ze & Wang, Yan & Ji, Zhicheng, 2020. "Synchronization of nonlinearly coupled complex networks: Distributed impulsive method," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).

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