摄动-增量法解Duffing-Van der Pol方程极限环  

Limit Cycles of Duffing-Van der Pol Equation by the Perturbation-incremental Method

作　　者：李军桦 汪海玲 李祖雄 LI Junhua;WANG Hailing;LI Zuxiong(School of Mathematics and Statistics,Hubei Minzu University,Enshi 445000,China;College of Mathematics and Statistics,Guangxi Normal University,Guilin 541004,China;College of Mathematics and Statistics,Chongqing Three Gorges University,Wanzhou 404199,China)

机构地区：[1]湖北民族大学数学与统计学院,湖北恩施445000 [2]广西师范大学数学与统计学院,广西桂林541004 [3]重庆三峡学院数学与统计学院,重庆万州404199

出　　处：《湖北民族大学学报（自然科学版）》2020年第3期297-302,共6页Journal of Hubei Minzu University:Natural Science Edition

基　　金：国家自然科学基金项目(11701163,11561022).

摘　　要：本文提出并应用摄动-增量法研究一类Duffing-Van der Pol方程的极限环,并给出对应参数时极限环的解析解和相图.该方法的特点是先应用摄动法,设出小参数λ,令λ≈0时,求极限环的零阶摄动解,然后应用谐波平衡法建立含Fourier级数展开式的线性代数方程组,再用参数增量法,将小参数的解延拓至大参数,并给出满足给定精确度的极限环的解析表达式,最后通过给出实例并与数值积分法作比较,验证该方法的有效性.In this paper we use the perturbation-incremental method to study the limit cycles of a Duffing-Van der Pol equation,and give the analytical solutions and the phase diagrams of limit cycles.The characteristics of this method are as follows:Firstly,the perturbation method is used to calculate the zero-order perturbation solution of limit cycles when the parameter is small,and the harmonic balance method is used to establish the linear algebraic equations of Fourier series expansion.Then,the demodulation of small parameters are extended to large parameters by using the parameter incremental method,and the analytic expression of limit cycles are given.Finally,an example is given and compared with the numerical integration method to verify the effectiveness of this method.

关 键 词：Duffing-Van der Pol方程 摄动-增量法 极限环 

分 类 号：O193[理学—数学]