Nonlinear Dynamics

, Volume 51, Issue 1, pp 171–181

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

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

DOI: 10.1007/s11071-007-9200-y

Cite this article as:
Mahmoud, G.M., Aly, S.A. & AL-Kashif, M.A. Nonlinear Dyn (2008) 51: 171. doi:10.1007/s11071-007-9200-y

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-scrollChaotic attractorChaosSynchronizationActive controlError systemComplex variablesDissipative dynamicsEquilibria and stability

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