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On differences and similarities in the analysis of Lorenz, Chen, and Lu systems

Author

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  • Leonov, G.A.
  • Kuznetsov, N.V.

Abstract

Currently it is being actively discussed the question of the equivalence of various Lorenz-like systems and the possibility of universal consideration of their behavior (Algaba et al., 2013a,b, 2014b,c; Chen, 2013; Chen and Yang, 2013; Leonov, 2013a), in view of the possibility of reduction of such systems to the same form with the help of various transformations. In the present paper the differences and similarities in the analysis of the Lorenz, the Chen and the Lu systems are discussed. It is shown that the Chen and the Lu systems stimulate the development of new methods for the analysis of chaotic systems. Open problems are discussed.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:256:y:2015:i:c:p:334-343
    DOI: 10.1016/j.amc.2014.12.132
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    References listed on IDEAS

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    1. Tigan, Gheorghe & Opriş, Dumitru, 2008. "Analysis of a 3D chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 36(5), pages 1315-1319.
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    Cited by:

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    4. Qasim M. Zainel & Saad M. Darwish & Murad B. Khorsheed, 2022. "Employing Quantum Fruit Fly Optimization Algorithm for Solving Three-Dimensional Chaotic Equations," Mathematics, MDPI, vol. 10(21), pages 1-21, November.
    5. Alexeeva, Tatyana A. & Kuznetsov, Nikolay V. & Mokaev, Timur N., 2021. "Study of irregular dynamics in an economic model: attractor localization and Lyapunov exponents," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    6. Čermák, Jan & Nechvátal, Luděk, 2019. "Stability and chaos in the fractional Chen system," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 24-33.
    7. Taheri, Alireza Ghomi & Setoudeh, Farbod & Tavakoli, Mohammad Bagher & Feizi, Esmaeil, 2022. "Nonlinear analysis of memcapacitor-based hyperchaotic oscillator by using adaptive multi-step differential transform method," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    8. Bayani, Atiyeh & Alexander, Prasina & Azarnoush, Hamed & Rajagopal, Karthikeyan & Jafari, Sajad & Nazarimehr, Fahimeh, 2023. "Designing networks with specific synchronization transitions independent of the system’s dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 632(P1).
    9. Li Xiong & Zhenlai Liu & Xinguo Zhang, 2017. "Dynamical Analysis, Synchronization, Circuit Design, and Secure Communication of a Novel Hyperchaotic System," Complexity, Hindawi, vol. 2017, pages 1-23, November.
    10. Fuchen Zhang & Rui Chen & Xiusu Chen, 2017. "Analysis of a Generalized Lorenz–Stenflo Equation," Complexity, Hindawi, vol. 2017, pages 1-6, December.
    11. Zhang, Fuchen & Shu, Yonglu, 2015. "Global dynamics for the simplified Lorenz system model," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 53-60.

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