Detecting period-doubling bifurcation: an approximate monodromy matrix approach

被引：11
|
作者：
Berns, DW
Moiola, JL
Chen, GR
机构：
[1] City Univ Hong Kong, Dept Elect Engn, Kowloon, Hong Kong, Peoples R China
[2] Univ Nacl Patagonia San Juan Bosco, Dept Ingn Elect, RA-9000 Comodoro Rivadavia, Argentina
[3] Univ Nacl Sur, CONICET, RA-8000 Bahia Blanca, Argentina
[4] Univ Nacl Sur, Dept Ingn Elect, RA-8000 Bahia Blanca, Argentina
来源：
AUTOMATICA | 2001年 / 37卷 / 11期
关键词：
differential equations; dynamic systems; feedback systems; frequency methods; harmonic balance; limit cycles; nonlinear control systems;
D O I：
10.1016/S0005-1098(01)00131-5
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
A quasi-analytical approach is developed for detecting period-doubling bifurcation emerging near a Hopf bifurcation point. The new algorithm employs higher-order Harmonic Balance Approximations (HBAs) to compute the monodromy matrix, useful for the study of limit cycle bifurcations. Prediction of the period-doubling bifurcation is accomplished very accurately by using this algorithm, along with a detailed approximation error analysis, without using numerical integration of the dynamical system. An example is given to illustrate the results. (C) 2001 Elsevier Science Ltd. All rights reserved.
引用
收藏
页码：1787 / 1795
页数：9
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