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Solution bounds of generalized Lorenz chaotic systems

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  • Sun, Yeong-Jeu

Abstract

In this paper, the generalized Lorenz chaotic system is considered and the solution bounds of such a system are investigated. Based on the time-domain approach, the upper solution bound and lower solution bound of the generalized Lorenz chaotic system are proposed. Finally, a numerical example is provided to illustrate the use of the main result.

Suggested Citation

  • Sun, Yeong-Jeu, 2009. "Solution bounds of generalized Lorenz chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 691-696.
    • Handle: RePEc:eee:chsofr:v:40:y:2009:i:2:p:691-696
    DOI: 10.1016/j.chaos.2007.08.015
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    References listed on IDEAS

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    1. Chen, Hsien-Keng, 2005. "Global chaos synchronization of new chaotic systems via nonlinear control," Chaos, Solitons & Fractals, Elsevier, vol. 23(4), pages 1245-1251.
    2. Luo, Albert C.J., 2006. "Predictions of quasi-periodic and chaotic motions in nonlinear Hamiltonian systems," Chaos, Solitons & Fractals, Elsevier, vol. 28(3), pages 627-649.
    3. Chien, Tsun-I & Liao, Teh-Lu, 2005. "Design of secure digital communication systems using chaotic modulation, cryptography and chaotic synchronization," Chaos, Solitons & Fractals, Elsevier, vol. 24(1), pages 241-255.
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    Cited by:

    1. Shu, Yonglu & Xu, Hongxing & Zhao, Yunhong, 2009. "Estimating the ultimate bound and positively invariant set for a new chaotic system and its application in chaos synchronization," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 2852-2857.
    2. Zhang, Fuchen & Shu, Yonglu & Yang, Hongliang & Li, Xiaowu, 2011. "Estimating the ultimate bound and positively invariant set for a synchronous motor and its application in chaos synchronization," Chaos, Solitons & Fractals, Elsevier, vol. 44(1), pages 137-144.
    3. Samia Rezzag & Fuchen Zhang, 2022. "On the Dynamics of New 4D and 6D Hyperchaotic Systems," Mathematics, MDPI, vol. 10(19), pages 1-10, October.
    4. Wang, Haijun & Li, Xianyi, 2018. "A note on “Hopf bifurcation analysis and ultimate bound estimation of a new 4-D quadratic autonomous hyper-chaotic system” in [Appl. Math. Comput. 291 (2016) 323–339] by Amin Zarei and Saeed Tavakoli," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 1-4.

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