Analytical Period-m Motions in a Parametric, Quadratic Nonlinear Oscillator

被引：0
|
作者：
Luo, Albert C. J. [1 ]
Yu, Bo [1 ]
机构：
[1] Southern Illinois Univ Edwardsville, Edwardsville, IL 62026 USA
来源：
COMPLEX MOTIONS AND CHAOS IN NONLINEAR SYSTEMS | 2016年 / 15卷
关键词：
MATHIEU-DUFFING OSCILLATOR;
D O I：
10.1007/978-3-319-28764-5_9
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Analytical solutions of period-m motions in a parametric quadratic nonlinear oscillator are obtained through the finite Fourier series, and the corresponding stability and bifurcation analysis for periodic motions are discussed. The bifurcation trees of periodic motions to chaos in a parametric oscillator with quadratic nonlinearity are presented. Numerical illustration shows good agreement between the analytical and numerical results.
引用
收藏
页码：247 / 258
页数：12
相关论文
共 50 条
  • [1] Analytical routes of period-m motions to chaos in a parametric, quadratic nonlinear oscillator
    Luo A.C.J.
    Yu B.
    International Journal of Dynamics and Control, 2016, 4 (1) : 1 - 22
  • [2] AN APPROXIMATE SOLUTION FOR PERIOD-M MOTIONS IN A PERIODICALLY FORCED OSCILLATOR WITH QUADRATIC NONLINEARITY
    Luo, Albert C. J.
    Yu, Bo
    PROCEEDINGS OF THE ASME INTERNATIONAL MECHANICAL ENGINEERING CONGRESS AND EXPOSITION, 2013, VOL 4B, 2014,
  • [3] Analytical solutions for period-m motions in a periodically forced van der Pol oscillator
    Luo A.C.J.
    Baghaei Lakeh A.
    International Journal of Dynamics and Control, 2013, 1 (2) : 99 - 115
  • [4] PERIOD-M MOTIONS IN A PERIODICALLY FORCED VAN DER POL OSCILLATOR
    Luo, Albert C. J.
    Lakeh, Arash Baghaei
    PROCEEDINGS OF THE ASME INTERNATIONAL MECHANICAL ENGINEERING CONGRESS AND EXPOSITION, 2013, VOL 4B, 2014,
  • [5] ANALYTICAL PERIODIC MOTIONS OF A PARAMETRIC OSCILLATOR WITH QUADRATIC NONLINEARITY
    Luo, Albert C. J.
    Yu, Bo
    PROCEEDINGS OF THE ASME INTERNATIONAL DESIGN ENGINEERING TECHNICAL CONFERENCES AND COMPUTERS AND INFORMATION IN ENGINEERING CONFERENCE, 2014, VOL 8, 2014,
  • [6] ANALYTICAL DYNAMICS OF PERIOD-m FLOWS AND CHAOS IN NONLINEAR SYSTEMS
    Luo, Albert C. J.
    Huang, Jianzhe
    INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2012, 22 (04):
  • [7] Bifurcation Trees of Periodic Motions to Chaos in a Parametric, Quadratic Nonlinear Oscillator
    Luo, Albert C. J.
    Yu, Bo
    INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2014, 24 (05):
  • [8] Period-m Motions to Chaos in a Periodically Forced, Duffing Oscillator with a Time-Delayed Displacement
    Luo, Albert C. J.
    Jin, Hanxiang
    INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2014, 24 (10):
  • [9] ANALYTICAL PERIOD-1 MOTIONS IN A PERIODICALLY FORCED OSCILLATOR WITH QUADRATIC NONLINEARITY
    Luo, Albert C. J.
    Yu, Bo
    INTERNATIONAL MECHANICAL ENGINEERING CONGRESS AND EXPOSITION - 2012, VOL 4, PTS A AND B, 2013, : 1011 - 1020
  • [10] Period-m motions and bifurcation trees in a periodically forced, van der Pol-Duffing oscillator
    Luo A.C.J.
    Lakeh A.B.
    International Journal of Dynamics and Control, 2014, 2 (04) : 474 - 493
12345