On cascades of bifurcations leading to chaos in several nonlinear dissipative systems of ODEs |
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| Institution: | 1. Organisation for the Strategic Coordination of Research and Intellectual Properties, Meiji University, 4-21-1 Nakano, Nakano-ku, Tokyo 164-8525, Japan;2. Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502, Japan;3. School of Mathematics & Statistics, University of St Andrews, St. Andrews, KY16 9SS, Scotland, UK;1. Departamento de Física Teórica and IUMA, Universidad de Zaragoza, c. Pedro Cerbuna 12, 50009 Zaragoza, Spain;2. Department of Mathematical Methods in Physics, University of Warsaw, ul. Pasteura 5, 02-093, Warszawa, Poland;1. School of Mathematics and Maxwell Institute for Mathematical Sciences, University of Edinburgh, Edinburgh EH9 3JZ, Scotland, UK;3. The University of Wollongong, Wollongong, NSW 2522, Australia;1. Faculty of Energy Technology, University of Maribor, Ho?evarjev trg 1, 8270 Kr?ko, Slovenia;2. Center for Applied Mathematics and Theoretical Physics, University of Maribor, Mladinska 3, SI-2000 Maribor, Slovenia;3. Faculty of Natural Sciences and Mathematics, University of Maribor, Koro?ka c. 160, 2000 Maribor, Slovenia;4. Departament de Matemàtica, Universitat de Lleida, Av. Jaume II, 69, 25001 Lleida, Catalonia, Spain |
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| Abstract: | This paper considers several nonlinear dissipative systems of ordinary differential equations. The studied systems undergo a full analysis of corresponding singular points on a whole set of parameters’ values variation. Specifically, types of singular points, boarders of stability regions, as well as presented local bifurcations, are determined. By using numerical methods a consideration of scenarios of transition to chaos in these systems with one bifurcation parameter variation is held. The aim of this research is a confirmation of a Feigenbaum–Sharkovskii–Magnitskii mechanism of transition to chaos unique for all dissipative systems of ODEs. As the result of analysis of one of the systems the lack of any chaotic behavior is shown with the help of Poincare sections. |
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