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Hyperchaos behaviors and chaos synchronization of two unidirectional coupled simplified Lorenz systems

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Abstract

To design a hyperchaotic generator and apply chaos into secure communication, a linear unidirectional coupling control is applied to two identical simplified Lorenz systems. The dynamical evolution process of the coupled system is investigated with variations of the system parameter and coupling coefficients. Particularly, the influence of coupling strength on dynamics of the coupled system is analyzed in detail. The range of the coupling strength in which the coupled system can generate hyperchaos or realize synchronization is determined, including phase portraits, Lyapunov exponents, and Poincaré section. And the critical value of the system parameter between hyperchaos and synchronization is also found with fixed coupled strength. In addition, abundant dynamical behaviors such as four-wing hyperchaotic, two-wing chaotic, single-wing coexisting attractors and periodic orbits are observed and chaos synchronization error curves are also drawn by varying system parameter c. Numerical simulations are implemented to verify the results of these investigations.

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Authors and Affiliations

  1. School of Physics and Electronics, Central South University, Changsha, 410083, China

    Ke-hui Sun  (孙克辉), Yan Wang  (汪艳) & Yan-li Wang  (王艳丽)

  2. School of Physics Science and Technology, Xinjiang University, Urumqi, 830046, China

    Ke-hui Sun  (孙克辉)

Authors
  1. Ke-hui Sun  (孙克辉)
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  2. Yan Wang  (汪艳)
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  3. Yan-li Wang  (王艳丽)
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Corresponding author

Correspondence to Ke-hui Sun  (孙克辉).

Additional information

Foundation item: Projects(61073187, 61161006) supported by the National Nature Science Foundation of China; Project supported by the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry, China

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Sun, Kh., Wang, Y. & Wang, Yl. Hyperchaos behaviors and chaos synchronization of two unidirectional coupled simplified Lorenz systems. J. Cent. South Univ. 21, 948–955 (2014). https://doi.org/10.1007/s11771-014-2023-3

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  • DOI: https://doi.org/10.1007/s11771-014-2023-3

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