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Dynamic Analysis of the Nonlinear Chaotic System with Multistochastic Disturbances

Author

Listed:
  • Lingling Geng
  • Yongguang Yu
  • Shuo Zhang

Abstract

The nonlinear chaotic system with multistochastic disturbances is investigated. Based on the orthogonal polynomial approximation, the method of transforming the system into an equivalent deterministic system is given. Then dynamic analysis of the nonlinear chaotic system with multistochastic disturbances can be reduced into that of its equivalent deterministic system. Especially, the Lorenz system with multistochastic disturbances is studied to demonstrate the feasibility of the given method. And its dynamic behaviors are gained including the phase portrait, the bifurcation diagram, the Poincaré section, and the maximum Lyapunov exponent.

Suggested Citation

  • Lingling Geng & Yongguang Yu & Shuo Zhang, 2014. "Dynamic Analysis of the Nonlinear Chaotic System with Multistochastic Disturbances," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnljam:v:2014:y:2014:i:1:n:610816
    DOI: 10.1155/2014/610816
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    References listed on IDEAS

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    1. Jin, Yanfei & Xu, Wei & Xu, Meng, 2005. "Stochastic resonance in an asymmetric bistable system driven by correlated multiplicative and additive noise," Chaos, Solitons & Fractals, Elsevier, vol. 26(4), pages 1183-1187.
    2. Chen, Hsien-Keng & Lin, Tsung-Nan & Chen, Juhn-Horng, 2005. "Dynamic analysis, controlling chaos and chaotification of a SMIB power system," Chaos, Solitons & Fractals, Elsevier, vol. 24(5), pages 1307-1315.
    3. Li, Wei & Xu, Wei & Zhao, Junfeng & Ma, Shaojuan, 2005. "Stochastic optimal control of first-passage failure for coupled Duffing–van der Pol system under Gaussian white noise excitations," Chaos, Solitons & Fractals, Elsevier, vol. 25(5), pages 1221-1228.
    4. Loong Soon Tee & Zabidin Salleh, 2013. "Dynamical Analysis of a Modified Lorenz System," Journal of Mathematics, Hindawi, vol. 2013, pages 1-8, December.
    5. Li, Wei & Xu, Wei & Zhao, Junfeng & Jin, Yanfei, 2007. "Stochastic stability and bifurcation in a macroeconomic model," Chaos, Solitons & Fractals, Elsevier, vol. 31(3), pages 702-711.
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    Cited by:

    1. Zhiqiang Cheng & Wencheng Wang & Yuezhang Dai & Lun Li, 2022. "A High‐Security Privacy Image Encryption Algorithm Based on Chaos and Double Encryption Strategy," Journal of Applied Mathematics, John Wiley & Sons, vol. 2022(1).

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