Numerical inclusion of exact periodic solutions for time delay Duffing equation
Numerical inclusion of exact periodic solutions for time delay Duffing equation
复制标题
时滞杜芬方程精确周期解的数值包含
DOI：
10.1016/j.cam.2019.112620
复制
发表时间：
2020
期刊：
影响因子：
--
通讯作者：
S. Oishi
中科院分区：
文献类型：
--
作者：
S. Oishi
给出了时滞自治Duffing方程精确周期解的数值包含结果。构造性隐函数定理用于包含由精确周期解组成的一维解流形。作为时滞的函数，给出了一个关于周期解个数的下界的猜想。当时滞小于30时，我们用数值计算证明了这一猜想，并在此基础上给出了强迫时滞Duffing方程周期解存在性的证明理论.受迫项为正弦波。应力是研究与外力同步的周期解的分岔。以时滞为参数，研究了周期解的丰富分支现象。特别地，在共振峰处观察到一种分形结构。
Numerical inclusion results for exact periodic solutions are presented for the time delay autonomous Duffing equations. Constructive implicit function theorem is used for including one dimensional solution manifolds consisting of exact periodic solutions. A conjecture of a lower bound for a number of periodic solutions is given as a function of the time delay. If the delay time is less than 30, we have proved this conjecture using verified numerical computations.Theory for proving the existence of periodic solutions of the forced delay Duffing equation is proposed based on the verified numerical computations. The forced term is sinusoidal waves. Stress is on a study of the bifurcation of periodic solutions synchronizing to the external forces. A rich bifurcation phenomena of periodic solutions are reported taking the delay time as parameters. Especially, a kind of fractal structure is observed concerning resonance peaks.