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On the generalized Lorenz canonical form

Author

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  • Čelikovský, Sergej
  • Chen, Guanrong

Abstract

This short note is to briefly introduce the new notion of generalized Lorenz canonical form (GLCF), which contains the classical Lorenz system and the newly discovered Chen system as two extreme cases, along with infinitely many chaotic systems in between. It also points out that some recently reported chaotic systems are special cases of the GLCF.

Suggested Citation

  • Čelikovský, Sergej & Chen, Guanrong, 2005. "On the generalized Lorenz canonical form," Chaos, Solitons & Fractals, Elsevier, vol. 26(5), pages 1271-1276.
    • Handle: RePEc:eee:chsofr:v:26:y:2005:i:5:p:1271-1276
    DOI: 10.1016/j.chaos.2005.02.040
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    Cited by:

    1. Sun, Fengyun & Zhao, Yi & Zhou, Tianshou, 2007. "Identify fully uncertain parameters and design controllers based on synchronization," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1677-1682.
    2. Wang, Xia, 2009. "Si’lnikov chaos and Hopf bifurcation analysis of Rucklidge system," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2208-2217.
    3. Huang, Kuifei & Yang, Qigui, 2009. "Stability and Hopf bifurcation analysis of a new system," Chaos, Solitons & Fractals, Elsevier, vol. 39(2), pages 567-578.
    4. Wang, Jiezhi & Chen, Zengqiang & Yuan, Zhuzhi, 2009. "Existence of a new three-dimensional chaotic attractor," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 3053-3057.
    5. Gao, Tiegang & Chen, Zengqiang & Gu, Qiaolun & Yuan, Zhuzhi, 2008. "A new hyper-chaos generated from generalized Lorenz system via nonlinear feedback," Chaos, Solitons & Fractals, Elsevier, vol. 35(2), pages 390-397.
    6. Yu, Simin & Tang, Wallace K.S., 2009. "Tetrapterous butterfly attractors in modified Lorenz systems," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1740-1749.
    7. Dong, Chengwei & Liu, Huihui & Jie, Qi & Li, Hantao, 2022. "Topological classification of periodic orbits in the generalized Lorenz-type system with diverse symbolic dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    8. Zhiqin Qiao & Xianyi Li, 2014. "Dynamical analysis and numerical simulation of a new Lorenz-type chaotic system," Mathematical and Computer Modelling of Dynamical Systems, Taylor & Francis Journals, vol. 20(3), pages 264-283, May.
    9. Qi, Guoyuan & Chen, Guanrong & Zhang, Yuhui, 2008. "On a new asymmetric chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 37(2), pages 409-423.
    10. Doungmo Goufo, Emile Franc, 2017. "Solvability of chaotic fractional systems with 3D four-scroll attractors," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 443-451.
    11. Liao, Xiaoxin & Xu, F. & Wang, P. & Yu, Pei, 2009. "Chaos control and synchronization for a special generalized Lorenz canonical system – The SM system," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2491-2508.
    12. Zhou, Xiaobing & Wu, Yue & Li, Yi & Wei, Zhengxi, 2008. "Hopf bifurcation analysis of the Liu system," Chaos, Solitons & Fractals, Elsevier, vol. 36(5), pages 1385-1391.
    13. Wang, Junwei & Zhao, Meichun & Zhang, Yanbin & Xiong, Xiaohua, 2007. "S˘i’lnikov-type orbits of Lorenz-family systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 375(2), pages 438-446.
    14. Jiang, Yongxin & Sun, Jianhua, 2007. "Si’lnikov homoclinic orbits in a new chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 32(1), pages 150-159.
    15. Xiong, Xiaohua & Wang, Junwei, 2009. "Conjugate Lorenz-type chaotic attractors," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 923-929.
    16. Zhou, Liangqiang & Chen, Fangqi, 2009. "Hopf bifurcation and Si’lnikov chaos of Genesio system," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1413-1422.
    17. Qi, Guoyuan & Chen, Guanrong & van Wyk, Michaël Antonie & van Wyk, Barend Jacobus & Zhang, Yuhui, 2008. "A four-wing chaotic attractor generated from a new 3-D quadratic autonomous system," Chaos, Solitons & Fractals, Elsevier, vol. 38(3), pages 705-721.
    18. Chen, Zengqiang & Yang, Yong & Yuan, Zhuzhi, 2008. "A single three-wing or four-wing chaotic attractor generated from a three-dimensional smooth quadratic autonomous system," Chaos, Solitons & Fractals, Elsevier, vol. 38(4), pages 1187-1196.
    19. Li, Damei & Wu, Xiaoqun & Lu, Jun-an, 2009. "Estimating the ultimate bound and positively invariant set for the hyperchaotic Lorenz–Haken system," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1290-1296.
    20. Mathale, D. & Doungmo Goufo, Emile F. & Khumalo, M., 2020. "Coexistence of multi-scroll chaotic attractors for fractional systems with exponential law and non-singular kernel," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    21. Qi, Guoyuan & van Wyk, Barend Jacobus & van Wyk, Michaël Antonie, 2009. "A four-wing attractor and its analysis," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 2016-2030.

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