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Bifurcation behavior of the generalized Lorenz equations at large rotation numbers. (English) Zbl 0897.76038

Summary: The bifurcation structure and periodic orbits of the Lorenz-Stenflo equations at large rotation numbers are given. It is shown that rotation can lead to a much richer dynamical behavior than that of the original Lorenz system, and can be used to control or modify the latter’s chaos behavior. Orbits with new topology arising from the merging and splitting of different periodic windows are observed. Abrupt changes in the one-dimensional map are pointed out and studied in terms of the interaction of the interior and exterior boundaries.

MSC:

76E30 Nonlinear effects in hydrodynamic stability
76U05 General theory of rotating fluids
37G99 Local and nonlocal bifurcation theory for dynamical systems
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