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

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.


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