Zhusubaliyev, Zhanybai T.; Soukhoterin, Evgeniy; Mosekilde, Erik Quasiperiodicity and torus breakdown in a power electronic dc/dc converter. (English) Zbl 1129.78016 Math. Comput. Simul. 73, No. 6, 364-377 (2007). Summary: This paper discusses the mechanisms of torus formation and torus destruction in a dc/dc converter with relay control and hysteresis. We establish a chart of the dynamical modes in the input voltage versus load resistance parameter plane. This chart displays several different torus bifurcations along with their associated resonance tongues where periodic dynamics is observed. We show how a quintruple-turn torus is transformed into a single-turn torus in a homoclinic bifurcation and examine different mechanisms of torus destruction (via horseshoe formation and through period doubling). Particular emphasis is paid to following the changes of the stable and unstable manifolds in detail. Cited in 14 Documents MSC: 78A55 Technical applications of optics and electromagnetic theory 34C23 Bifurcation theory for ordinary differential equations Keywords:dc/dc converter with relay control hysteresis; quasiperiodicity breakdown; homoclinic bifurcations PDFBibTeX XMLCite \textit{Z. T. Zhusubaliyev} et al., Math. Comput. Simul. 73, No. 6, 364--377 (2007; Zbl 1129.78016) Full Text: DOI References: [1] Afraimovich, V. S.; Shilnikov, L. P., Invariant two-dimensional tori, their breakdown and stochasticity, Am. Math. Soc. Transl., 149, 2, 201-212 (1991) · Zbl 0751.58024 [2] Anishchenko, V. S., Dynamical Chaos — Models and Experiments (1995), World Scientific: World Scientific Singapore · Zbl 0866.58053 [3] Anishchenko, V. S.; Safonova, M. A.; Chua, L. O., Confirmation of the Afraimovich-Shilnikov torus-breakdown theorem via a torus circuit, IEEE Trans. Circ. Syst. I: Fund. Theory Appl., 40, 11, 792 (1993) · Zbl 0845.34053 [4] Arnold, V. I.; Afraimovich, V. S.; Il’yashenko, Y. 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