1∶2 INTERNAL RESONANCE OF COUPLED DYNAMIC SYSTEM WITH QUADRATIC AND CUBIC NONLINEARITIES  

作　　者：陈予恕 杨彩霞 吴志强 陈芳启 

出　　处：《Applied Mathematics and Mechanics(English Edition)》2001年第8期917-924,共8页应用数学和力学（英文版）

基　　金：theNationalNaturalScienceFoundationofChina ( 1 9990 51 0 ) ;theNationalKeyBasicResearchSpecialFund (G1 9980 2 0 3 1 6 ) ;theDoctoralPointFundofEducationCommitteeofChina (D0 990 1 )

摘　　要：The 1:2 internal resonance of coupled dynamic system with quadratic and cubic nonlinearities is studied. The normal forms of this system in 1 :2 internal resonance were derived by using the direct method of normal form. In the normal,forms, quadratic and cubic nonlinearities were remained. Based on a new convenient transformation technique, the 4-dimension bifurcation equations were reduced to 3-dimension. A bifurcation equation with one-dimension was obtained. Then the bifurcation behaviors of a universal unfolding were studied by using the singularity theory. The method of this paper can be applied to analyze the bifurcation behavior in strong internal resonance on 4-dimension center manifolds.The 1:2 internal resonance of coupled dynamic system with quadratic and cubic nonlinearities is studied. The normal forms of this system in 1 :2 internal resonance were derived by using the direct method of normal form. In the normal,forms, quadratic and cubic nonlinearities were remained. Based on a new convenient transformation technique, the 4-dimension bifurcation equations were reduced to 3-dimension. A bifurcation equation with one-dimension was obtained. Then the bifurcation behaviors of a universal unfolding were studied by using the singularity theory. The method of this paper can be applied to analyze the bifurcation behavior in strong internal resonance on 4-dimension center manifolds.

关 键 词：quadratic and cubic nonlinearities Normal Form 1 : 2 internal resonance 

分 类 号：O193[理学—数学] O177.91[理学—基础数学]