Nonlinear Dynamics

, Volume 69, Issue 4, pp 1979–1994 | Cite as

Dynamics analysis and hybrid function projective synchronization of a new chaotic system

  • Xiangjun Wu
  • Shanzhi Li
Original Paper


This paper introduces a novel three-dimensional autonomous chaotic system by adding a quadratic cross-product term to the first equation and modifying the state variable in the third equation of a chaotic system proposed by Cai et al. (Acta Phys. Sin. 56:6230, 2007). By means of theoretical analysis and computer simulations, some basic dynamical properties, such as Lyapunov exponent spectrum, bifurcations, equilibria, and chaotic dynamical behaviors of the new chaotic system are investigated. Furthermore, hybrid function projective synchronization (HFPS) of the new chaotic system is studied by employing three different synchronization methods, i.e., adaptive control, system coupling and active control. The proposed approaches are applied to achieve HFPS between two identical new chaotic systems with fully uncertain parameters, HFPS in coupled new chaotic systems, and HFPS between the integer-order new chaotic system and the fractional-order Lü chaotic system, respectively. Corresponding numerical simulations are provided to validate and illustrate the analytical results.


Chaos Lyapunov exponent Bifurcation Hybrid function projective synchronization (HFPS) Uncertain parameter Fractional-order chaotic system 



This research was jointly supported by the National Natural Science Foundation of China (Grant No. 61004006), the Natural Science Foundation of Henan Province, China (Grant No. 112300410009), the Foundation for University Young Key Teacher Program of Henan Province, China (Grant No. 2011GGJS-025), and the Natural Science Foundation of Educational Committee of Henan Province, China (Grant No. 2011A520004).


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Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Department of Computing Center, Institute of Complex Intelligent Network SystemHenan UniversityKaifengChina
  2. 2.School of Computer and Information EngineeringHenan UniversityKaifengChina

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