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Hyperchaos evolved from the generalized Lorenz equation. (English) Zbl 1079.34032

Summary: A new hyperchaotic system is formulated by introducing an additional state into the third-order generalized Lorenz equation. The existence of the hyperchaos is verified with bifurcation analysis, and the bifurcation routes from periodic, quasi-periodic, chaotic and hyperchaotic evolutions are observed. Various attractors are illustrated not only by computer simulation but also by the realization of an electronic circuit.

MSC:

34C28 Complex behavior and chaotic systems of ordinary differential equations
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
34C23 Bifurcation theory for ordinary differential equations
34D45 Attractors of solutions to ordinary differential equations
34C60 Qualitative investigation and simulation of ordinary differential equation models
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