Bogdanov-Takens bifurcation in an oscillator with positive damping and multiple delays
Bogdanov-Takens bifurcation in an oscillator with positive damping and multiple delays
复制标题
具有正阻尼和多重延迟的振荡器中的 Bogdanov-Takens 分岔
DOI：
10.1007/s11071-016-3040-6
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发表时间：
2017
影响因子：
5.6
通讯作者：
Liang Jinling
中科院分区：
文献类型：
--
作者：
Wang Jinling;Liu Xia;Liang Jinling
本文研究了具有多重时滞的阻尼谐振子。导出了系统的原点为Bogdanov-Takens（B-T）奇点的存在条件.通过中心流形约化和选择合适的分岔参数，得到了系统B-T分岔的二阶和三阶规范形。最后，数值模拟来说明理论准则。
In this paper, a damped harmonic oscillator with multiple delays is investigated. The existence conditions under which the origin of the system is a Bogdanov–Takens (B–T) singularity are derived. By utilizing the center manifold reduction and choosing suitable bifurcation parameters, the second- and the third-order normal forms of the B–T bifurcation for the system are obtained. Finally, numerical simulations are presented to illustrate the theoretical criteria.