The European Physical Journal Special Topics

, Volume 223, Issue 8, pp 1591–1600 | Cite as

Dynamics of fractional-order sinusoidally forced simplified Lorenz system and its synchronization

  • Yan Wang
  • Kehui SunEmail author
  • Shaobo He
  • Huihai Wang
Regular Article Synchronization of Systems and Networks for Communication
Part of the following topical collections:
  1. Chaos, Cryptography and Communications


In this paper, dynamical behaviors of the fractional-order sinusoidally forced simplified Lorenz are investigated by employing the time-domain solution algorithm of fractional-order calculus. The system parameters and the fractional derivative orders q are treated as bifurcation parameters. The range of the bifurcation parameters in which the system generates chaos is determined by bifurcation, phase portrait, and Poincaré section, and different bifurcation motions are visualized by virtue of a systematic numerical analysis. We find that the lowest order of this system to yield chaos is 3.903. Based on fractional-order stability theory, synchronization is achieved by using nonlinear feedback control method. Simulation results show the scheme is effective and a chaotic secure communication scheme is present based on this synchronization.


Phase Portrait European Physical Journal Special Topic Bifurcation Diagram Chaotic Attractor Lorenz System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© EDP Sciences and Springer 2014

Authors and Affiliations

  1. 1.School of Physics and Electronics, Central South UniversityChangshaPR China
  2. 2.School of Physics Science and Technology, Xinjiang UniversityUrumchiPR China

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