Bifurcation trees of period-1 motions in a periodically excited, softening Duffing oscillator with time-delay

被引：0

作者：

Xing S. ^{[1
]}

Luo A.C.J. ^{[1
]}

机构：

[1] Department of Mechanical and Industrial Engineering, Southern Illinois University Edwardsville, Edwardsville, 62026-1805, IL

来源：

International Journal of Dynamics and Control | 2019年 / 7卷 / 03期

关键词：

Bifurcation tree; Frequency–amplitude characteristics; Implicit mapping; Mapping structures; Period-1 motions to chaos; Time-delay softening Duffing oscillator;

D O I：

10.1007/s40435-019-00520-1

中图分类号：

学科分类号：

摘要：

In this paper, bifurcation trees of period-1 motions to chaos in a periodically excited, time-delay, softening Duffing oscillator are analytically predicted through an implicit mapping method. Discretization of the time-delay oscillator gives an implicit mapping. Stable and unstable periodic motions in such a time-delay, softening Duffing oscillator are achieved through the corresponding mapping structures. From the finite discrete Fourier series, harmonic frequency–amplitude characteristics for stable and unstable solutions of period-1 to period-4 motions are developed, and the singularity, catastrophes and quantity levels of harmonic amplitudes are presented. A symmetric period-1 motion with symmetric break generates three branches of period-1 motions to chaos. From the analytical prediction, periodic motions in the time-delay softening Duffing oscillator are simulated numerically. The bifurcation trees of period-1 motions to chaos in the time-delay softening Duffing oscillator are difficult to be obtained from the traditional analytical methods. © 2019, Springer-Verlag GmbH Germany, part of Springer Nature.

引用

页码：842 / 855

页数：13

共 27 条

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