A hyperchaotic complex Chen system and its dynamics. (English) Zbl 1136.37327

Mahmoud, Gamal M.; Mahmoud, Emad E.; Ahmed, Mansour E.

Int. J. Appl. Math. Stat. 12, No. D07, 90-100 (2007).

Summary: The main goal of this article is to introduce and study the dynamics of a new hyperchaotic complex Chen system. The dynamics of this system which is a 6-dimensional autonomous system is rich and complicated. The new system has chaotic, hyperchaotic attractors, periodic, quasi-periodic solutions and the solutions approach fixed points. These solutions are calculated based on Lyapunov exponents. Bifurcation diagram of this system are calculated and in good agreement with Lyapunov exponents. Different hyperchaotic complex Chen systems are suggested. Our results are demonstrated graphically.

MSC:

37D45	Strange attractors, chaotic dynamics of systems with hyperbolic behavior
37C10	Dynamics induced by flows and semiflows
37G99	Local and nonlocal bifurcation theory for dynamical systems
34C28	Complex behavior and chaotic systems of ordinary differential equations
34C25	Periodic solutions to ordinary differential equations
34C27	Almost and pseudo-almost periodic solutions to ordinary differential equations
34D20	Stability of solutions to ordinary differential equations

Keywords:

complex nonlinear behavior; chaos; periodic solutions; hyperchaotic attractors; quasi-periodic solutions; fixed points; Lyapunov exponents; bifurcation diagram