CAJ | 학술논문

在双曲函数摄动法的基础上，推广双曲函数Lindstedt-Poincaré(L-P)法的适用范围，使之适用于定量分析一类含五次强非线性项的自激振子的同宿分岔和同宿解问题。以双曲函数系为基础推导出适用于高次非线性系统的摄动步骤，对极限环的同宿分岔参数进行摄动展开，给出同宿摄动解奇异项的定义，以消除同宿摄动解奇异项作为确定极限环同宿分岔点的条件，给出能够严格满足同宿条件的同宿轨道摄动解。算例表明，在相平面内该方法的结果与Runge-Kutta法数值周期轨道的逼近结果比较吻合。
재쌍곡함수섭동법적기출상，추엄쌍곡함수Lindstedt-Poincaré(L-P)법적괄용범위，사지괄용우정량분석일류함오차강비선성항적자격진자적동숙분차화동숙해문제。이쌍곡함수계위기출추도출괄용우고차비선성계통적섭동보취，대겁한배적동숙분차삼수진행섭동전개，급출동숙섭동해기이항적정의，이소제동숙섭동해기이항작위학정겁한배동숙분차점적조건，급출능구엄격만족동숙조건적동숙궤도섭동해。산례표명，재상평면내해방법적결과여Runge-Kutta법수치주기궤도적핍근결과비교문합。
Based on the previous studies on hyperbolic perturbation methods,the hyperbolic Lindstedt-Poincaré (L-P) method was extended for homoclinic solution and homoclinic bifurcation analysis of strongly nonlinear self-excited oscillators. By adopting the hyperbolic functions instead of traditional periodic functions in the L-P method,the perturbation procedure for high-power strongly nonlinear system was derived. The homoclinic bifurcation values for limit cycle were expanded in power of perturbation parameter, the secular terms of the perturbation homoclinic solutions were defined. The homoclinic bifurcation values were then determined by eliminating the secular terms. The homoclinic solutions which satisfy the homoclinic conditions were given. The solutions of the phase planes and bifurcation values of some typical examples were obtained. It showed that the results by the presented method were in agreement with those of the Runge-Kutta numerical method. Thus, the accuracy and efficiency of the present method was verified.