BIFURCATION SOLUTIONS OF RESONANT CASES OF NONLINEAR MATHIEU EQUATIONS

作     者：陈予恕 梅林涛 

作者机构：Tianjin University Tianjin 300072 PRC The Second Designing Institute Ministry of Nuclear Industry Beijing 100840 PRC 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：1990年第33卷第12期

页      面：1469-1476页

核心收录：

学科分类：07[理学] 08[工学] 

基　　金：Project supported by the National Natural Science Foundation of China 

主　　题：resonance bifurcation solution nonlinear Mathieu equation symmetry. 

摘      要：The bifurcation solutions of resonant cases, including the main resonance, subharmonic resonance, superharmonic resonance and fractional resonance, are studied with the Liapunov-Schmidt method. The (α’,β’)-plane of every resonant case divides into six open regions; all points inside any one of the six regions give topologically equivalent response diagrams. The boundary arcs separating these six regions are of two distinct types: five of them are of the normal codimension-1 and one is of infinite codimensions. The theoretical base of vibration, control of nonlinear systems is presented.