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Analysis of a Lorenz-Like Chaotic System by Lyapunov Functions

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  • Fuchen Zhang

Abstract

In this paper, we investigate the ultimate bound set and positively invariant set of a 3D Lorenz-like chaotic system, which is different from the well-known Lorenz system, Rössler system, Chen system, Lü system, and even Lorenz system family. Furthermore, we investigate the global exponential attractive set of this system via the Lyapunov function method. The rate of the trajectories going from the exterior of the globally exponential attractive set to the interior of the globally exponential attractive set is also obtained for all the positive parameters values . The innovation of this paper is that our approach to construct the ultimate bounded and globally exponential attractivity sets assumes that the corresponding sets depend on some artificial parameters ( and ); that is, for the fixed parameters of the system, we have a series of sets depending on and . The results contain the known result as a special case for the fixed and . The efficiency of the scheme is shown numerically. The theoretical results may find wide applications in chaos control and chaos synchronization.

Suggested Citation

  • Fuchen Zhang, 2019. "Analysis of a Lorenz-Like Chaotic System by Lyapunov Functions," Complexity, Hindawi, vol. 2019, pages 1-6, July.
    • Handle: RePEc:hin:complx:7812769
    DOI: 10.1155/2019/7812769
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    References listed on IDEAS

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    1. Wang, Xingyuan & Wang, Mingjun, 2008. "A hyperchaos generated from Lorenz system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(14), pages 3751-3758.
    2. Qi, Guoyuan & Chen, Guanrong & Du, Shengzhi & Chen, Zengqiang & Yuan, Zhuzhi, 2005. "Analysis of a new chaotic system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 352(2), pages 295-308.
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    Cited by:

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    2. Jiri Petrzela & Miroslav Rujzl, 2022. "Chaotic Oscillations in Cascoded and Darlington-Type Amplifier Having Generalized Transistors," Mathematics, MDPI, vol. 10(3), pages 1-25, February.

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