Nonlinear Dynamics

, Volume 67, Issue 2, pp 987–996

On the boundedness of solutions to the Lorenz-like family of chaotic systems

  • Chunlai Mu
  • Fuchen Zhang
  • Yonglu Shu
  • Shouming Zhou
Original Paper

DOI: 10.1007/s11071-011-0041-3

Cite this article as:
Mu, C., Zhang, F., Shu, Y. et al. Nonlinear Dyn (2012) 67: 987. doi:10.1007/s11071-011-0041-3

Abstract

This paper deals with a class of three-dimensional autonomous nonlinear systems which have potential applications in secure communications, and investigates the localization problem of compact invariant sets of a class of Lorenz-like chaotic systems which contain T system with the help of iterative theorem and Lyapunov function theorem. Since the Lorenz-like chaotic system does not have y in the second equation, the approach used to the Lorenz system cannot be applied to the Lorenz-like chaotic system. We overcome this difficulty by introducing a cross term and get an interesting result, which includes the most interesting case of the chaotic attractor of the Lorenz-like systems. Furthermore, the results obtained in this paper are applied to study complete chaos synchronization. Finally, numerical simulations show the effectiveness of the proposed scheme.

Keywords

Lorenz-like systems The boundedness Lyapunov function theorem 

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  • Chunlai Mu
    • 1
  • Fuchen Zhang
    • 1
  • Yonglu Shu
    • 1
  • Shouming Zhou
    • 1
  1. 1.College of Mathematics and StatisticsChongqing UniversityChongqingP.R. China

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