Rodríguez-Bernal, Aníbal; Van Vleck, Erik S. Complex oscillations in a closed thermosyphon. (English) Zbl 1004.34035 Int. J. Bifurcation Chaos Appl. Sci. Eng. 8, No. 1, 41-56 (1998). Summary: The dynamics of a closed thermosyphon are considered. Using an explicit construction, obtained through an inertial manifold, exact low-dimensional models are derived. The behavior of solutions is analyzed for different ranges of the relevant parameters, and the Lorenz model is obtained for a range of parameter values. Numerical experiments are performed for three- and five-mode models. Cited in 1 ReviewCited in 4 Documents MSC: 34C60 Qualitative investigation and simulation of ordinary differential equation models 34C45 Invariant manifolds for ordinary differential equations 34C28 Complex behavior and chaotic systems of ordinary differential equations PDFBibTeX XMLCite \textit{A. Rodríguez-Bernal} and \textit{E. S. Van Vleck}, Int. J. Bifurcation Chaos Appl. Sci. Eng. 8, No. 1, 41--56 (1998; Zbl 1004.34035) Full Text: DOI References: [1] DOI: 10.1016/0017-9310(92)90317-L · doi:10.1016/0017-9310(92)90317-L [2] DOI: 10.1115/1.3247510 · doi:10.1115/1.3247510 [3] DOI: 10.1007/BF01612888 · Zbl 0387.76052 · doi:10.1007/BF01612888 [4] DOI: 10.1016/0022-0396(88)90110-6 · Zbl 0643.58004 · doi:10.1016/0022-0396(88)90110-6 [5] DOI: 10.1115/1.3451057 · doi:10.1115/1.3451057 [6] DOI: 10.1115/1.3247511 · doi:10.1115/1.3247511 [7] Herrero M. A., J. Appl. Math. 1 pp 1– (1990) [8] DOI: 10.1115/1.3268269 · doi:10.1115/1.3268269 [9] DOI: 10.1016/S0065-2717(08)70061-3 · doi:10.1016/S0065-2717(08)70061-3 [10] DOI: 10.1007/BF01221359 · Zbl 0443.76059 · doi:10.1007/BF01221359 [11] DOI: 10.1017/S0022112066001423 · doi:10.1017/S0022112066001423 [12] DOI: 10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2 · Zbl 1417.37129 · doi:10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2 [13] Lorenz E. N., Grmela, M. & Marsden, J. E. (1979) [14] Malkus W. V. R., Mémoires Société Royale des Sciences de Liège, Series 6 pp 125– (1972) [15] DOI: 10.1006/jmaa.1995.1276 · Zbl 0854.76088 · doi:10.1006/jmaa.1995.1276 [16] DOI: 10.1115/1.3247533 · doi:10.1115/1.3247533 [17] DOI: 10.1137/S0036139993246787 · Zbl 0823.35151 · doi:10.1137/S0036139993246787 [18] DOI: 10.1016/0017-9310(90)90005-F · doi:10.1016/0017-9310(90)90005-F [19] DOI: 10.1017/S0022112067000606 · Zbl 0163.20702 · doi:10.1017/S0022112067000606 [20] DOI: 10.1007/BF01011469 · doi:10.1007/BF01011469 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.