中文摘要：

本文提出一个新的摄动法，称为双曲函数摄动法，它适合于求解非线性自治系统的同（异）宿轨线。具体研究具有三次非线性的自治系统x^-＋c1x＋c3x^3=εf（μ,x,x^·），阐述双曲函数摄动法求解同（异）宿轨线的过程。该法在求解过程中还能同时确定存在同（异）宿轨线的参数μ。以两个广义Lienard方程为典型算例，双曲函数摄动法求得的同宿轨线与Runge-Kutta方法求得的结果非常吻合，说明了双曲函数摄动法是求非线性自治系统同（异）宿轨线的有效方法。

英文摘要：

A hyperbolic perturbation method was presented for determining the homoclinic and heteroclinic solutions of certain strongly nonlinear autonomous oscillators in the form x^-＋c1x＋c3x^3=εf（μ,x,x^·）, in which the hyperbolic functions can be employed instead of the usual periodic functions in the usual perturbation procedure. The value of μ, under which there exists a homoclinic or heteroclinic solution of oscillator, can be determined in the perturbation procedure. The generalized Lienard oscillator with f（μ, x, x^·） = （μ -μ1x^2 -μ2x^·2）x^· was studied. Comparisons with numerical simulations （Runge-Kutta method） illustrate the present method is provided with efficiency and accuracy.