Implementation and Analysis of a Simple Circuit Causing Border-Collision Bifurcation

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  • Border-Collision分岐を呈する簡素な回路の実現と解析
  • Border Collision ブンキ オ テイスル カンソ ナ カイロ ノ ジツゲン ト カイセキ

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Abstract

Recently, a new type of bifurcation phenomena called Border-Collision (abbr. BC) bifurcation has been discovered for one or two-dimensional one-parameter families of discrete-time systems. A skewed tent map is the simplest model exhibiting the BC bifurcation and the existence of break point (undifferentiable point) in the map is an essential for BC bifurcation. In some continuous systems, BC bifurcation is also confirmed. In particular, many interesting bifurcation phenomena including BC bifurcation are observed in the power electronic systems. Since power electronic circuits with current or voltage feedback have wide industrial applications, indeed, theoretical and experimental analysis in such systems are very important in practical point of view. In this paper, we propose a system interrupted by own state and a periodic interval, and show that the system has much variety of bifurcation phenomena, including BC bifurcation. To analyze properties of the dynamics, we derive a one-dimensional map explicitly. We show some theorem and the regions of periodic solution within two parameter space. Some of theoretical results are verified by laboratory experiments.

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