一类RLC电路模型解的定性分析  

Qualitative analysis of the solution to a kind of RLC circuit model

作　　者：格日措毛[1] 

机构地区：[1]青海师范大学民族师范学院数学系,青海西宁810008

出　　处：《青海师范大学学报（自然科学版）》2010年第4期17-21,24,共6页Journal of Qinghai Normal University(Natural Science Edition)

摘　　要：在电路分析中经常会遇到一些阻尼振荡电路,由于这类电路在高压断路器开断能力测试、受控热核研究等许多重要的工程领域有着极为广泛的应用,因此有必要对此类电路的特性加以讨论,研究.本文对一类特殊的二维非线性动力系统的定性特征进行了研究,这类二维动力系统来自对非线性RLC电路的振荡特性的描述.我们首先利用maple对系统的平衡点、向量场、相图特征进行了实验,然后利用动力系统的理论和方法讨论了平衡点的稳定性,系统的分支特征及极限环的存在性,唯一性和稳定性.并由此解释了相应RLC电路的振荡特性.With the development of electronic technology,more and more coupled systems of electricity-magnetism-mechanism are used widely.These coupled systems have abundant non-linear dynamics phenomena.In order to improve stability and security of operation of these systems,we ought to study these systems in detail.Damping-oscillatory circuits are often encountered in the fields of circuit analysis.It is necessary to discuss and deliberate this type of circuit because they are widely used in many important fields of engineering,such as the switch test of high-voltage circuit-breaker,the research of controllable thermonuclear reaction,etc.First the paper introduces how to establish the mathematical model and then presents the property of the modal,such as the stability of fixed points,the existent of limit cycles.We also interpret the physical meaning of the results.

关 键 词：相平面 平衡点 极限环 HOPF分歧 

分 类 号：O59[理学—应用物理]