The Stabilizing mechanism for an interrupted dynamical system with periodic threshold

被引：3

作者：

Asahara, Hiroyuki ^{[1
]}

Tasaki, Kenichi ^{[1
]}

Aihara, Kazuyuki ^{[2
]}

Kousaka, Takuji ^{[1
]}

机构：

[1] Oita Univ, Dept Engn, 700 Dannoharu, Oita 8701192, Japan

[2] Univ Tokyo, Inst Ind Sci, Meguro Ku, Tokyo 1538505, Japan

来源：

IEICE NONLINEAR THEORY AND ITS APPLICATIONS | 2012年 / 3卷 / 04期

基金：

日本学术振兴会;

关键词：

interrupted dynamical system; periodic threshold; fixed threshold; bifurcation; return map; stability;

D O I：

10.1587/nolta.3.546

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This study mathematically analyzes an interrupted dynamical system (IDS) with a periodic threshold. First, we describe a simple IDS, which is dependent on its own state and a periodic interval, and explain the behavior of the waveform. Then, we define the discrete map (return map) of the system and calculate the bifurcation diagrams. Finally, we focus on the dynamical structure of the return map in the system with a periodic threshold and discuss the stabilizing mechanism, especially its effect in a wide parameter space. The stabilizing effect is verified by the laboratory experiment.

引用

页码：546 / 556

页数：11

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