| HOPF分叉定理在非线性振荡电路中的应用 |
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| 引用本文： | 李义府,谢长焱,蔡自兴. HOPF分叉定理在非线性振荡电路中的应用[J]. 湖南师范大学自然科学学报, 2002, 25(1): 34-36,40 |
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| 作者姓名： | 李义府 谢长焱 蔡自兴 |
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| 作者单位： | 中南大学信息科学与工程学院电子科学与技术系,中国长沙,410083 |
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| 基金项目： | 国家自然科学基金 (6 99740 43)，湖南省自然科学基金 (99JJY2 0 0 6 2 )资助项目 |
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| 摘 要： | 利用李雅普诺夫函数推导的HOPF分叉定理时域型式中的综合参数－曲率系数a0和其二维系统中的局部型式来分析二阶自治非线性电路中的振荡问题。通过列出电路的状态方程计算其雅可比矩阵共轭复数特征值和求出曲率系数，并判别系统是否具有稳定的极限环来判断电路是否会出现自激振荡，从而为电子线路的振荡分析提供一种新的分析方法。
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| 关 键 词： | 曲率系数 极限环 李雅普诺夫函数 状态方程 非线性振荡电路 HOPF分叉定理 自激振荡 |
| 文章编号： | 1000-2537(2002)01-0034-03 |
Application Research of HOPF Bifurcation Theorem in Nonlinear Oscillation Circuits |
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| LI Yi-fu,XIE Chang-yan,CAI Zi-xing. Application Research of HOPF Bifurcation Theorem in Nonlinear Oscillation Circuits[J]. Journal of Natural Science of Hunan Normal University, 2002, 25(1): 34-36,40 |
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| Authors: | LI Yi-fu XIE Chang-yan CAI Zi-xing |
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| Abstract: | By using Lyapnov function the synthetic parameter, i.e. coefficient of curvature of HOPF bifurcation theorem, in time domain is derived, the oscillation of second order autonomous nonlinear circuit is analyzed by means of the local type of two-dimension system of the theorem, a couple of complex eigenvalues of Jacob matrix of the state equations for the circuit and the coefficient of curvature are calculated by use of the state equations, then whether or not a circuit will occur self-oscillation can be judged through judging that if there exist a steady limit cycle, in the circuit in this paper. As a result, a new method for analyzing the oscillation of the electronic circuits is provided. |
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| Keywords: | Coefficient of curvature limit cycles Lyapmov function state equation |
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