Alternate pacing of border-collision period-doubling bifurcations

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• 作者：Xiaopeng Zhao and David G. Schaeffer
• 关键词：Bifurcation identification ; Border ; collision bifurcations ; Alternate pacing ; Prebifurcation amplification ; Cardiac dynamics
• 刊名：Nonlinear Dynamics
• 出版年：2007
• 出版时间：November, 2007
• 年：2007
• 卷：50
• 期：3
• 页码：733-742
• 全文大小：335 KB
• 刊物类别：Engineering
• 刊物主题：Vibration, Dynamical Systems and Control
  Mechanics
  Mechanical Engineering
  Automotive and Aerospace Engineering and Traffic
  
• 出版者：Springer Netherlands
• ISSN：1573-269X

文摘

Unlike classical bifurcations, border-collision bifurcations occur when, for example, a fixed point of a continuous, piecewise C 1 map crosses a boundary in state space. Although classical bifurcations have been much studied, border-collision bifurcations are not well understood. This paper considers a particular class of border-collision bifurcations, i.e., border-collision period-doubling bifurcations. We apply a subharmonic perturbation to the bifurcation parameter, which is also known as alternate pacing, and we investigate the response under such pacing near the original bifurcation point. The resulting behavior is characterized quantitatively by a gain, which is the ratio of the response amplitude to the applied perturbation amplitude. The gain in a border-collision period-doubling bifurcation has a qualitatively different dependence on parameters from that of a classical period-doubling bifurcation. Perhaps surprisingly, the differences are more readily apparent if the gain is plotted versus the perturbation amplitude (with the bifurcation parameter fixed) than if plotted versus the bifurcation parameter (with the perturbation amplitude fixed). When this observation is exploited, the gain under alternate pacing provides a useful experimental tool to identify a border-collision period-doubling bifurcation.