Universal classification of bifurcating solutions to a primary parametric resonance in van der Pol-Duffing-Mathicu's systems  

作　　者：陈予恕 徐鉴 

机构地区：[1]Department of Mechanics, Tianjin University, Tianjin 300072, China [2]Department of Applied Physico-Mathematics, Beijing University of Aero-Astronautics, Beijing 100083, China

出　　处：《Science China Mathematics》1996年第4期405-417,共13页中国科学：数学（英文版）

基　　金：the National Natural Science Foundation of China and National Education Committee of China Science Foundation.

摘　　要：The bifurcation of the second-order approximate solutions of nonlinear parametrically excited systems possessing generalized van der Pol's dampings and quintic Duffing's nonlinearities subjected to a primary parametric resonance is investigated. Using singularity theory with Z2-symmetry, bifurcations of the solutions are universally classified in a topologically equivalent sense for Z2-codimension>3. The question of whether the approximate solutions from the classical perturbation methods can be topologically equivalent in describing the periodic responses and the bifurcations of the original systems is made clear. The numerical results indicate that the vibration characteristic may suddenly disappear in the range of Z2-codimension>4.The bifurcation of the second-order approximate solutions of nonlinear parametrically excited systems possessing generalized van der Pol’s dampings and quintic Duffing’s nonlinearities subjected to a primary parametric resonance is investigated. Using singularity theory with Z2-symmetry, bifurcations of the solutions are universally classified in a topologically equivalent sense for Z2-codimension>3. The question of whether the approximate solutions from the classical perturbation methods can be topologically equivalent in describing the periodic responses and the bifurcations of the original systems is made clear. The numerical results indicate that the vibration characteristic may suddenly disappear in the range of Z2-codimension>4.

关 键 词：dynamical SYSTEM TOPOLOGICAL EQUIVALENCE nonlinear parametrically excited SYSTEM BIFURCATION universal unfolding. 

分 类 号：O19[理学—数学]