Nonlinear Dynamics

, Volume 51, Issue 1–2, pp 171–181 | Cite as

Dynamical properties and chaos synchronization of a new chaotic complex nonlinear system

  • Gamal M. Mahmoud
  • Shaban A. Aly
  • M. A. AL-Kashif
Original Paper

Abstract

In this paper, we introduce a new chaotic complex nonlinear system and study its dynamical properties including invariance, dissipativity, equilibria and their stability, Lyapunov exponents, chaotic behavior, chaotic attractors, as well as necessary conditions for this system to generate chaos. Our system displays 2 and 4-scroll chaotic attractors for certain values of its parameters. Chaos synchronization of these attractors is studied via active control and explicit expressions are derived for the control functions which are used to achieve chaos synchronization. These expressions are tested numerically and excellent agreement is found. A Lyapunov function is derived to prove that the error system is asymptotically stable.

Keywords

2 and 4-scroll Chaotic attractor Chaos Synchronization Active control Error system Complex variables Dissipative dynamics Equilibria and stability 

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Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  • Gamal M. Mahmoud
    • 1
  • Shaban A. Aly
    • 1
  • M. A. AL-Kashif
    • 2
  1. 1.Department of MathematicsFaculty of Science, Assiut UniversityAssiutEgypt
  2. 2.Department of MathematicsFaculty of Science, AL-Azhar UniversityAssiutEgypt

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