Arnold tongues in a billiard problem in nonlinear and nonequilibrium systems

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• 作者：Tomoyuki Miyaji ^{tmiyaji@meiji.ac.jp}
• 关键词：Nonlinear and nonequilibrium system ; Billiard problem ; Hopf&ndash ; Hopf bifurcation ; Arnold tongues
• 刊名：Physica D: Nonlinear Phenomena
• 出版年：2017
• 出版时间：1 February 2017
• 年：2017
• 卷：340
• 期：Complete
• 页码：14-25
• 全文大小：2325 K
• 卷排序：340

文摘

A model of spot dynamics of a reaction–diffusion system in a rectangle is studied. Numerical and analytical methods are employed. Periodic trajectories in a rectangle are characterized by rotation numbers. The Neimark–Sacker bifurcation of a limit cycle and Arnold tongues are found. The Hopf–Hopf bifurcation is an organizing center of complex bifurcation structure.