Dynamical properties and chaos synchronization of a new chaotic complex nonlinear system. (English) Zbl 1170.70365

Mahmoud, Gamal M.; Aly, Shaban A.; Al-Kashif, M. A.

Nonlinear Dyn. 51, No. 1-2, 171-181 (2008).

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:

70K55	Transition to stochasticity (chaotic behavior) for nonlinear problems in mechanics
70K20	Stability for nonlinear problems in 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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