Torus Break-down and Bifurcations in Coupled Oscillators

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• 作者：Ferdinand Verhulst ; ^{f.verhulst@uu.nl" class="auth_mail" title="E-mail the corresponding author}
• 关键词：periodic solutions ; bifurcations ; quasi-periodic solutions ; tori ; chaos
• 刊名：Procedia IUTAM
• 出版年：2016
• 出版时间：2016
• 年：2016
• 卷：19
• 期：Complete
• 页码：5-10
• 全文大小：187 K

文摘

To discover qualitative changes of solutions of differential equations, one has to study their bifurcations. We start with the well- known bifurcations of equilibria leading to periodic solutions, followed by bifurcations of periodic solutions (Neimark-Sacker and Hopf-Hopf) in a dissipative setting leading to quasi-periodic motion corresponding with tori. In their turn these families of quasi-periodic solutions may bifurcate to produce strange attractors. A number of examples illustrate the theory.