Pei Qin-yuan, Li Li. Chaotic Behavior of Forced Oscillator Containing a Square Nonlinear Term on Principal Resonance Curves[J]. Applied Mathematics and Mechanics, 1995, 16(3): 217-223.
 Citation: Pei Qin-yuan, Li Li. Chaotic Behavior of Forced Oscillator Containing a Square Nonlinear Term on Principal Resonance Curves[J]. Applied Mathematics and Mechanics, 1995, 16(3): 217-223.

# Chaotic Behavior of Forced Oscillator Containing a Square Nonlinear Term on Principal Resonance Curves

• Rev Recd Date: 1994-10-06
• Publish Date: 1995-03-15
• Based on [1],we investigate the route to chaos in forced oscillator containing a square nonlinear term on principal resonance curves. And chaotic motion is observed against the background of classical resonance curves,stability limits and jump phenomena.It is shown that chaotic motion appears in the neighbourhood of the point both meeting condition that Melnikov function has simple zero and having the point of vertical tangent of the resonance curves.
•  [1] 裴钦元、李骊,一个非线性振子的浑沌现象,应用数学和力学,14(5)(1993),377-388. [2] Guokenheimer,J.and P.J.Holmes,Nonlinear oscillations,dynamical systems and bifurcations of vector fields. Revised and Corrected,SPringer-Verlay (1986). [3] 李继彬、刘曾荣,一类二次系数周期扰动的浑沌性质,科学通报,7(1985),491-495. [4] 李继彬、刘曾荣,几类非线性受迫振动系统的浑沌性质,数学物理学报,5(1986),195-204. [5] 林常,有限个次谐分叉导致浑沌的一个例子,科学通报,(1985),980-982. [6] Szemplinska-Stupnicka,W.,Bifurcations of harmonic solution leading to chaotic motion in the softening type duffing's oscillator,Int,J. Nonlinear Mechanics,23(1988),257-277 [7] Szemplinska-Stupnicka,W.and P.Niezgodzki,The approximate approach to chaos phenomena in oscillators having single equilibrium position,l ,Sound and Vibraiion,14(1990),181-192. [8] Minorsky,N.,Introduction to Nonlinear Mechanics,J,W,Edwards,Ann,Arbor,Mich,(1947). [9] Nayfeh,A.H. and D,T. Mook,Nonlinear Oscillations,John Wiley,New York.(1979).

### Catalog

###### 通讯作者: 陈斌, bchen63@163.com
• 1.

沈阳化工大学材料科学与工程学院 沈阳 110142