Dynamics of a hyperchaotic Lorenz system. (English) Zbl 1143.37309

Barboza, Ruy

Int. J. Bifurcation Chaos Appl. Sci. Eng. 17, No. 12, 4285-4294 (2007).

Summary: In this paper, we investigate the dynamics of the Lorenz system, linearly extended into one additional dimension. The system is hyperchaotic in a wide range of parameters. A theoretical and numerical study indicates that chaos and hyperchaos are produced with the help of a van der Pol-like oscillatory motion around a hypersaddle stationary point at the origin. Numerical experiments are presented, showing Lyapunov exponents, bifurcation diagrams and Poincaré sections.

MSC:

37D45	Strange attractors, chaotic dynamics of systems with hyperbolic behavior
34C28	Complex behavior and chaotic systems of ordinary differential equations

Keywords:

chaos; hyperchaos; Lorenz system

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