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Global dynamics for the simplified Lorenz system model

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  • Zhang, Fuchen
  • Shu, Yonglu

Abstract

In this paper, the global attractive sets of the simplified Lorenz system are studied according to Lyapunov stability theory. The method for constructing the Lyapunov functions that applied to the former chaotic systems does not work for the simplified Lorenz system. We overcome this difficulty by adding a cross term to the Lyapunov functions of the simplified Lorenz system.

Suggested Citation

  • Zhang, Fuchen & Shu, Yonglu, 2015. "Global dynamics for the simplified Lorenz system model," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 53-60.
    • Handle: RePEc:eee:apmaco:v:259:y:2015:i:c:p:53-60
    DOI: 10.1016/j.amc.2015.01.122
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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. 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.
    3. 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.
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    Cited by:

    1. Zhang, Fuchen, 2015. "On a model of the dynamical systems describing convective fluid motion in rotating cavity," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 873-882.

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