Nonlinear Dynamics

, Volume 78, Issue 1, pp 279–288 | Cite as

Hopf bifurcation analysis of a new commensurate fractional-order hyperchaotic system

  • Xiang Li
  • Ranchao Wu
Original Paper


In this paper, a new fractional-order hyperchaotic system based on the Lorenz system is presented. The chaotic behaviors are validated by the positive Lyapunov exponents. Furthermore, the fractional Hopf bifurcation is investigated. It is found that the system admits Hopf bifurcations with varying fractional order and parameters, respectively. Under different bifurcation parameters, some conditions ensuring the Hopf bifurcations are proposed. Numerical simulations are given to illustrate and verify the results.


Lorenz system Chaos Fractional-order system Hopf bifurcation Stability 



The authors would like to thank the reviewers and the editor for their valuable comments and suggestions. This work is supported by the Program of National Natural Science Foundation of China (No. 51275229), the Specialized Research Fund for the Doctoral Program of Higher Education of China (No. 20093401120001).


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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.State Key Laboratory of Mechanics and Control of Mechanical StructuresNanjing University of Aeronautics and AstronauticsNanjing China
  2. 2.School of MathematicsAnhui UniversityHefei China

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