Confusion threshold study of the Duffing oscillator with a nonlinear fractional damping term

被引：4
|
作者：
Mei-Qi, Wang [1 ,2 ]
Wen-Li, Ma [1 ,2 ]
En-Li, Chen [1 ,2 ]
Shao-Pu, Yang [1 ,2 ]
Yu-Jian, Chang [3 ]
Zhang, Wanjie [1 ,2 ,3 ]
机构：
[1] Shijiazhuang Tiedao Univ, State Key Lab Mech Behav & Syst Safety Traff Engn, Shijiazhuang, Hebei, Peoples R China
[2] Shijiazhuang Tiedao Univ, Sch Mech Engn, Shijiazhuang, Hebei, Peoples R China
[3] Shijiazhuang Tiedao Univ, Sch Elect & Elect Engn, Shijiazhuang, Hebei, Peoples R China
来源：
JOURNAL OF LOW FREQUENCY NOISE VIBRATION AND ACTIVE CONTROL | 2021年 / 40卷 / 02期
基金：
中国国家自然科学基金;
关键词：
Nonlinear damping; fractional derivative; Duffing oscillator; stability; FRACTAL CALCULUS; SYNCHRONIZATION; EXPLANATION; TRANSFORM; POL; VAN;
D O I：
10.1177/1461348420922686
中图分类号：
O42 [声学];
学科分类号：
070206 ; 082403 ;
摘要：
In this study, the critical conditions for generating chaos in a Duffing oscillator with nonlinear damping and fractional derivative are investigated. The Melnikov function of the Duffing oscillator is established based on Melnikov theory. The necessary analytical conditions and critical value curves of chaotic motion in the sense of Smale horseshoe are obtained. The numerical solutions of chaotic motion, including time history diagram, frequency spectrum diagram, phase diagram, and Poincare map, are studied. The correctness of the analytical solution is verified through a comparison of numerical and analytical calculations. The effects of linear and nonlinear parameters on chaotic motion are also analyzed. These results are relevant to the study of system dynamics.
引用
收藏
页码：929 / 947
页数：19
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