Donner, Reik; Feudel, Fred; Seehafer, Norbert; Sanjuán, Miquel A. F. Hierarchical modeling of a forced Roberts dynamo. (English) Zbl 1141.37380 Int. J. Bifurcation Chaos Appl. Sci. Eng. 17, No. 10, 3589-3593 (2007). Summary: We investigate the dynamo effect in a flow configuration introduced by G. O. Roberts [Philos. Trans. roy. Soc. London, Ser. A 271, 411–454 (1972; Zbl 0235.76061)]. Based on a clear energetic hierarchy of Fourier components on the steady-state dynamo branch, an approximate model of interacting modes is constructed covering all essential features of the complete system but allowing simulations with a minimum amount of computation time. We use this model to study the excitation mechanism of the dynamo, the transition from stationary to time-dependent dynamo solutions and the characteristic properties of the latter ones. Cited in 1 Document MSC: 37N20 Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics) 93A30 Mathematical modelling of systems (MSC2010) 37G99 Local and nonlocal bifurcation theory for dynamical systems Citations:Zbl 0235.76061 PDFBibTeX XMLCite \textit{R. Donner} et al., Int. J. Bifurcation Chaos Appl. Sci. Eng. 17, No. 10, 3589--3593 (2007; Zbl 1141.37380) Full Text: DOI References: [1] DOI: 10.1016/S0375-9601(97)00319-8 · Zbl 1053.37517 · doi:10.1016/S0375-9601(97)00319-8 [2] DOI: 10.1103/PhysRevE.54.2589 · doi:10.1103/PhysRevE.54.2589 [3] DOI: 10.1103/PhysRevE.68.046302 · doi:10.1103/PhysRevE.68.046302 [4] DOI: 10.1103/PhysRevLett.84.4365 · doi:10.1103/PhysRevLett.84.4365 [5] Moffatt H. K., Magnetic Field Generation in Electrically Conducting Fluids (1978) [6] DOI: 10.1098/rsta.1972.0015 · doi:10.1098/rsta.1972.0015 [7] DOI: 10.1103/PhysRevE.57.5533 · doi:10.1103/PhysRevE.57.5533 [8] DOI: 10.1063/1.1331315 · Zbl 1184.76529 · doi:10.1063/1.1331315 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.