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Analysis of a 3D chaotic system

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  • Tigan, Gheorghe
  • Opriş, Dumitru

Abstract

A 3D nonlinear chaotic system, called the T system, is analyzed in this paper. Horseshoe chaos is investigated via the heteroclinic Shilnikov method constructing a heteroclinic connection between the saddle equilibrium points of the system. Partially numerical computations are carried out to support the analytical results.

Suggested Citation

  • Tigan, Gheorghe & Opriş, Dumitru, 2008. "Analysis of a 3D chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 36(5), pages 1315-1319.
    • Handle: RePEc:eee:chsofr:v:36:y:2008:i:5:p:1315-1319
    DOI: 10.1016/j.chaos.2006.07.052
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    References listed on IDEAS

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    1. Álvarez, G. & Li, Shujun & Montoya, F. & Pastor, G. & Romera, M., 2005. "Breaking projective chaos synchronization secure communication using filtering and generalized synchronization," Chaos, Solitons & Fractals, Elsevier, vol. 24(3), pages 775-783.
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    Cited by:

    1. Tigan, Gheorghe & Constantinescu, Dana, 2009. "Heteroclinic orbits in the T and the Lü systems," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 20-23.
    2. Wu, Yue & Zhou, Xiaobing & Chen, Jia & Hui, Bei, 2009. "Chaos synchronization of a new 3D chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1812-1819.
    3. Li, Xian-Feng & Chu, Yan-Dong & Zhang, Jian-Gang & Chang, Ying-Xiang, 2009. "Nonlinear dynamics and circuit implementation for a new Lorenz-like attractor," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2360-2370.
    4. Li, Xian-Feng & Chu, Yan-Dong & Leung, Andrew Y.T. & Zhang, Hui, 2017. "Synchronization of uncertain chaotic systems via complete-adaptive-impulsive controls," Chaos, Solitons & Fractals, Elsevier, vol. 100(C), pages 24-30.
    5. Wu, Ranchao & Fang, Tianbao, 2015. "Stability and Hopf bifurcation of a Lorenz-like system," Applied Mathematics and Computation, Elsevier, vol. 262(C), pages 335-343.
    6. Loong Soon Tee & Zabidin Salleh, 2013. "Dynamical Analysis of a Modified Lorenz System," Journal of Mathematics, Hindawi, vol. 2013, pages 1-8, December.
    7. Yang, Shuangling & Qu, Jingjia, 2021. "On first integrals of a family of generalized Lorenz-like systems," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    8. Assali, El Abed, 2021. "Predefined-time synchronization of chaotic systems with different dimensions and applications," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    9. Leonov, G.A. & Kuznetsov, N.V., 2015. "On differences and similarities in the analysis of Lorenz, Chen, and Lu systems," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 334-343.

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