Chaotic vibrations of the duffing system with fractional damping

被引：61

作者：

Syta, Arkadiusz ^{[1
]}

Litak, Grzegorz ^{[1
]}

Lenci, Stefano ^{[2
]}

Scheffler, Michael ^{[3
]}

机构：

[1] Lublin Univ Technol, Fac Mech Engn, PL-20618 Lublin, Poland

[2] Polytech Univ Marche, Dept Civil & Bldg Engn & Architecture, I-60131 Ancona, Italy

[3] Tech Univ Dresden, Inst Festkorpermech, D-01062 Dresden, Germany

来源：

CHAOS | 2014年 / 24卷 / 01期

基金：

欧盟第七框架计划;

关键词：

IDENTIFICATION;

D O I：

10.1063/1.4861942

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We examined the Duffing system with a fractional damping term. Calculating the basins of attraction, we demonstrate a broad spectrum of non-linear behaviour connected with sensitivity to the initial conditions and chaos. To quantify dynamical response of the system, we propose the statistical 0-1 test as well as the maximal Lyapunov exponent; the application of the latter encounter a few difficulties because of the memory effect due to the fractional derivative. The results are confirmed by bifurcation diagrams, phase portraits, and Poincare sections. (C) 2014 AIP Publishing LLC.

引用

页码：1 / 6

页数：6

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