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Zbl 1170.70365
Mahmoud, Gamal M.; Aly, Shaban A.; Al-Kashif, M.A.
Dynamical properties and chaos synchronization of a new chaotic complex nonlinear system. (English)
[J] Nonlinear Dyn. 51, No. 1-2, 171-181 (2008). ISSN 0924-090X; ISSN 1573-269X/e

Summary: 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.

MSC 2000:: *70K55 Transition to stochasticity (chaotic behavior)
70K20 Stability of nonlinear oscillations (general mechanics)

Keywords: 2 and 4-scroll; chaotic attractor; chaos; synchronization; active control; error system; complex variables; dissipative dynamics; equilibria and stability

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