Nonlinear Dynamics of Duffing System With Fractional Order Damping

被引：60

作者：

Cao, Junyi ^{[1
]}

Ma, Chengbin ^{[2
]}

Xie, Hang ^{[1
]}

Jiang, Zhuangde ^{[1
]}

机构：

[1] Xi An Jiao Tong Univ, State Key Lab Mfg Syst Engn, Res Inst Diagnost & Cybernet, Xian 710049, Peoples R China

[2] Shanghai Jiao Tong Univ, Univ Michigan, Joint Inst, Shanghai 200240, Peoples R China

来源：

JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS | 2010年 / 5卷 / 04期

基金：

中国国家自然科学基金; 中国博士后科学基金;

关键词：

bifurcation; calculus; chaos; damping; nonlinear dynamical systems; phase diagrams; Runge-Kutta methods; CHAOTIC DYNAMICS; TIME-DOMAIN; OSCILLATOR; BEHAVIOR; MODEL; VAN;

D O I：

10.1115/1.4002092

中图分类号：

TH [机械、仪表工业];

学科分类号：

0802 ;

摘要：

In this paper, nonlinear dynamics of Duffing system with fractional order damping is investigated. The fourth-order Runge-Kutta method and tenth-order CFE-Euler method are introduced to simulate the fractional order Duffing equations. The effect of taking fractional order on system dynamics is investigated using phase diagram, bifurcation diagram and Poincareacute map. The bifurcation diagram is introduced to exam the effect of excitation amplitude, frequency, and damping coefficient on the Duffing system with fractional order damping. The analysis results show that the fractional order damped Duffing system exhibits periodic motion, chaos, periodic motion, chaos, and periodic motion in turn when the fractional order varies from 0.1 to 2.0. The period doubling bifurcation route to chaos and inverse period doubling bifurcation out of chaos are clearly observed in the bifurcation diagrams with various excitation amplitude, frequency, and damping coefficient. [DOI: 10.1115/1.4002092]

引用

页码：1 / 6

页数：6

共 34 条

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