Zhou, Cangtao; Lai, C. H.; Yu, M. Y. Bifurcation behavior of the generalized Lorenz equations at large rotation numbers. (English) Zbl 0897.76038 J. Math. Phys. 38, No. 10, 5225-5239 (1997). 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. Cited in 1 ReviewCited in 14 Documents MSC: 76E30 Nonlinear effects in hydrodynamic stability 76U05 General theory of rotating fluids 37G99 Local and nonlocal bifurcation theory for dynamical systems Keywords:interaction of interior and exterior boundaries; Lorenz-Stenflo equations; merging; splitting; one-dimensional map PDF BibTeX XML Cite \textit{C. Zhou} et al., J. Math. Phys. 38, No. 10, 5225--5239 (1997; Zbl 0897.76038) Full Text: DOI OpenURL References: [1] DOI: 10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2 · Zbl 1417.37129 [2] DOI: 10.1016/0375-9601(75)90353-9 [3] DOI: 10.1088/0031-8949/43/5/019 [4] DOI: 10.1103/PhysRevA.29.2928 [5] DOI: 10.1088/0031-8949/31/1/003 · Zbl 1063.37530 [6] DOI: 10.1088/0031-8949/53/1/015 [7] DOI: 10.1088/0031-8949/54/2/003 · Zbl 0947.37023 [8] DOI: 10.1088/0031-8949/54/4/001 · Zbl 1063.37532 [9] DOI: 10.1016/0167-2789(83)90126-4 · Zbl 0561.58029 [10] DOI: 10.1016/0167-2789(83)90126-4 · Zbl 0561.58029 [11] DOI: 10.1103/PhysRevA.32.1222 [12] DOI: 10.1007/BFb0069804 [13] DOI: 10.1016/0167-2789(82)90016-1 · Zbl 1194.37155 [14] DOI: 10.1103/PhysRevLett.64.1196 · Zbl 0964.37501 [15] DOI: 10.1093/imanum/13.2.263 · Zbl 0769.65041 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.