摘要
非线性动力学发展过程中有三大著名方程,其中之一的V an der Po l方程,迄今一直都是理论与应用领域内探讨的热门课题.本文利用非线性系统相平面分析法和数学软件M athem atica 5.1,对V an der Po l方程的奇点、极限环的性质以及稳定性[1]展开较全面的探讨,从而获得该非线性系统受参数扰动的运动性状况以及在奇点附近轨线的运动规律.
Van der Pol equation is one of three famous equations in nonlinear dynamics, and is also a hot topic in both theory and application. The singular point and property of limit cycle of Van der Pol equation are analyzed thoroughly. The motional state of Van der Pol system is obtained, and the system is disturbed by parameter μ. The motional rules of the orbits around singular points are presented.
出处
《黄冈师范学院学报》
2006年第6期26-31,共6页
Journal of Huanggang Normal University
关键词
稳定性
极限环
特征根
非线性微分方程
stahility
limit cycle
eigenvalue
nonlinear differential equation
