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Chaos synchronization of two stochastic Duffing oscillators by feedback control

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  • Wu, Cunli
  • Fang, Tong
  • Rong, Haiwu

Abstract

This paper addresses chaos synchronization of two identical stochastic Duffing oscillators with bounded random parameters subject to harmonic excitations. In the analysis the stochastic Duffing oscillator is first transformed into an equivalent deterministic nonlinear system by Gegenbauer polynomial approximation, so that the chaos synchronization problem of stochastic Duffing oscillators can be reduced into that of the equivalent deterministic systems. Then a feedback control strategy is adopted to synchronize chaotic responses of two identical equivalent deterministic systems under different initial conditions. The feedback parameters are determined through analysis of the top Lyapunov exponent of the variational equation of the controlled responding system. Numerical analysis shows that the feedback control strategy is an effective way to synchronize two identical stochastic Duffing systems.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:32:y:2007:i:3:p:1201-1207
    DOI: 10.1016/j.chaos.2005.11.042
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    References listed on IDEAS

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    1. 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.
    2. Wu, Cunli & Lei, Youming & Fang, Tong, 2006. "Stochastic chaos in a Duffing oscillator and its control," Chaos, Solitons & Fractals, Elsevier, vol. 27(2), pages 459-469.
    3. Chen, Hsien-Keng, 2005. "Global chaos synchronization of new chaotic systems via nonlinear control," Chaos, Solitons & Fractals, Elsevier, vol. 23(4), pages 1245-1251.
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    2. Salarieh, Hassan & Alasty, Aria, 2008. "Adaptive chaos synchronization in Chua's systems with noisy parameters," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(3), pages 233-241.
    3. Zelinka, Ivan & Senkerik, Roman & Navratil, Eduard, 2009. "Investigation on evolutionary optimization of chaos control," Chaos, Solitons & Fractals, Elsevier, vol. 40(1), pages 111-129.
    4. Wu, Wenjuan & Chen, Zengqiang & Yuan, Zhuzhi, 2009. "The evolution of a novel four-dimensional autonomous system: Among 3-torus, limit cycle, 2-torus, chaos and hyperchaos," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2340-2356.
    5. 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.

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