非自治旋转机械系统的混沌及其混沌同步  

CHAOS AND CHAOS SYNCHRONIZATION FOR A NON-AUTONOMOUS ROTATIONAL MACHINE SYSTEM

作　　者：褚衍东[1] 张建刚[1] 李险峰[1] 常迎香[1] 

机构地区：[1]兰州交通大学数理与软件工程学院,兰州730070

出　　处：《机械强度》2010年第4期536-541,共6页Journal of Mechanical Strength

基　　金：国家自然科学基金(50475109);甘肃省自然科学基金(3ZS051-A25-030;3ZS-042-B25-049);甘肃省财政厅省属高校基本科研业务费专项基金(620004)资助~~

摘　　要：研究机械式离心调速器系统的复杂动力学行为。通过系统运动的拉格朗日方程和牛顿第二定律,建立机械式离心调速器系统的动力学方程。借助Poincar啨截面和Lyapunov指数研究系统的混沌行为,通过仿真系统的分岔图和Poincar啨截面,分析系统通向混沌的道路,并且验证该系统的分岔图与Lyapunov指数谱是完全吻合的。通过对系统施加两种不同的非线性反馈控制器,并选取合适的反馈系数,使得驱动与响应系统同步。数值模拟验证该方法的有效性。The complex dynamic behavior of the mechanical centrifugal flywheel govemor system is studied. The dynamical equation of the system is established using Lagrangian and Newton＇ s second law. The chaotic behavior of the system is analyzed by means of Poincar6 sections and the Lyapunov exponents. The evolution from Hopf bifurcation to chaos is shown by the bifurcation dia- grams and a series of Poincare sections under different sets of system parameters, and the bifurcation diagrams are verified by the related Lyapunov exponent spectra. Two different non-linear feedback-control systems with selected feedback-parameters are designed for synchronizing response system and drive system. Finally, the numerical simulations illustrate the effectiveness of the proposed scheme.

关 键 词：离心调速器 LYAPUNOV指数 混沌 混沌同步 Poincar啨截面 

分 类 号：O322[理学—一般力学与力学基础] TH113.1[理学—力学]