振动筛系统的Hopf-Hopf-Flip分岔与混沌演化  

HOPF-HOPF-FLIP BIFURCATION AND ROUTES TO CHAOS OF A SHAKER SYSTEM

作　　者：张永祥[1] 孔贵芹 俞建宁[3] 

机构地区：[1]沈阳农业大学理学院,辽宁沈阳110161 [2]中国船舶工业第6354研究所,江西九江332000 [3]兰州交通大学数理与软件工程学院,甘肃兰州730070

出　　处：《工程力学》2009年第1期233-237,共5页Engineering Mechanics

基　　金：甘肃省自然科学基金重点项目(3ZS051-A25-030);沈阳农业大学青年教师科研基金项目(2006212)

摘　　要：建立了振动筛系统的动力学模型和周期运动的六维Poincaré映射,基于Poincaré映射方法和数值仿真分析了此系统在余维三分岔点附近的动力学行为。研究了其Jacobian矩阵两对复共轭特征值和一负实特征值同时穿越单位圆情况下的Hopf-Hopf-Flip分岔,该系统在此类余维三分岔点附近存在周期运动的Hopf分岔、Flip分岔、环面分岔以及"五角星形"概周期吸引子,揭示了环面倍化以及分形出"五角星形"概周期吸引子并向混沌演化的两种非常规过程,它对于振动筛系统的动力学优化设计提供了理论参考。The dynamical model and six-dimensional Poincar6 maps of a shaker system are established in this paper firstly. Then, using Poincar6 maps and numerical integral method, this paper investigates its local codimension-3 bifurcation, concerning the case of two complex conjugate pairs of eigenvalues and a negative eigenvalue oflinearized map escaping the unit circle simultaneously. Local behaviors of the system, near the point of Hopf-Hopf-Flip bifurcation, are studied, where Hopf bifurcation occurs, as well as Flip bifurcation, toms bifurcation and ＂pentagram＂ attractor in projected Poincare sections. The routes to chaos via toms-doubling bifurcation and gradual fractalization of torus represented by ＂pentagram＂ attractor are analyzed by numerical simulation. The system parameters of a shaker may be optimized by studying the stability and bifurcation of periodic motion.

关 键 词：振动筛 余维三 POINCARÉ映射 Hopf-Hopf-Flip分岔 环面分岔 混沌 

分 类 号：O322[理学—一般力学与力学基础]