The Forced van der Pol Equation I: The Slow Flow and Its Bifurcations
The Forced van der Pol Equation I: The Slow Flow and Its Bifurcations
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DOI：
10.1137/s1111111102404738
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发表时间：
2003
期刊：
影响因子：
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通讯作者：
J. Guckenheimer;Kathleen A. Hoffman;Warren Weckesser
中科院分区：
文献类型：
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作者：
J. Guckenheimer;Kathleen A. Hoffman;Warren Weckesser
受迫货车der Pol振荡器是近世纪来科学界关注的焦点，但其全局分岔结构至今仍知之甚少。在本文中，我们提出了一个混合动力系统的动力学的轨迹上的慢流形耦合的“跳跃”的折叠在临界流形上的快速子系统。该混合系统的不动点和周期点的全局分岔导致了对受迫货车der Pol系统周期轨道（无鸭翼）分岔的理解。
The forced van der Pol oscillator has been the focus of scientific scrutiny for almost a century, yet its global bifurcation structure is still poorly understood. In this paper, we present a hybrid system consisting of the dynamics of the trajectories on the slow manifold coupled with "jumps" at the folds in the critical manifold to approximate the fast subsystem. The global bifurcations of the fixed points and periodic points of this hybrid system lead to an understanding of the bifurcations in the periodic orbits (without canards) of the forced van der Pol system.