Mathematical Problems in Engineering 
Volume 2005 (2005), Issue 3, Pages 365-375
doi:10.1155/MPE.2005.365

Escape time from potential wells of strongly nonlinear oscillators with slowly varying parameters

Jianping Cai,1 Y. P. Li,2 and Xiaofeng Wu2

 1Department of Mathematics, Zhangzhou Teachers College, Fujian 363000, China
2Department of Mathematics, Zhongshan University, Guangzhou 510275, China
Received 29 July 2004; Revised 7 October 2004

Abstract

The effect of negative damping to an oscillatory system is to force the amplitude to increase gradually and the motion will be out of the potential well of the oscillatory system eventually. In order to deduce the escape time from the potential well of quadratic or cubic nonlinear oscillator, the multiple scales method is firstly used to obtain the asymptotic solutions of strongly nonlinear oscillators with slowly varying parameters, and secondly the character of modulus of Jacobian elliptic function is applied to derive the equations governing the escape time. The approximate potential method, instead of Taylor series expansion, is used to approximate the potential of an oscillation system such that the asymptotic solution can be expressed in terms of Jacobian elliptic function. Numerical examples verify the efficiency of the present method.