一类离心调速器的超混沌及其混沌同步  

Hyperchaotic and Chaos synchronization for A Type of Centrifugal Governor

作　　者：杨丽新[1] 何万生[1] 褚衍东[2] 张建刚[2] 李险峰[2] 

机构地区：[1]天水师范学院数学与统计学院,天水741001 [2]兰州交通大学数理与软件工程学院,兰州730070

出　　处：《武汉理工大学学报（交通科学与工程版）》2009年第6期1219-1223,共5页Journal of Wuhan University of Technology（Transportation Science & Engineering）

基　　金：国家自然科学基金项目(批准号:50475109);甘肃省自然科学基金项目(批准号:3ZS-042-B25-049)资助

摘　　要：通过Lyapunov指数研究了系统的超混沌行为,应用仿真系统的分岔图和Poincaré截面分析了系统通向混沌的道路,并且验证了该系统的分岔图与Lyapunov指数谱是吻合的.基于Laypunov稳定性理论,设计了一种非线性控制器,理论上证明了超混沌系统的自同步,数值仿真进一步验证了该控制方案的有效性.The complex dynamic behavior of the centrifugal flywheel governor system subjected to external disturbance is studied. By mechanics analyzing, the dynamical equation of the system are established, the characteristic of hyperchaotic attractors of the system are analyzed by the phase portraits. Lyapunov exponents are presented to analyze hyperchaotic behavior of the system. The hyperchaotic behavior of system of two positive Lyapunov exponents along with one zero and one negative Lyapunov exponent is obtained. Routes from Hopf bifurcation to chaos are analyzed by the bifurcation diagram and Poincare sections, and the Lyapunov exponents corresponded to bifurcation diagrams of the system are confirmed. Based on Lyapunov theory, a nonlinear controller is designed to synchronization two identical systems, numerical simulations show the effectiveness of the proposed method.

关 键 词：调速器 LYAPUNOV指数 POINCARÉ截面 分岔 超混沌 混沌同步 

分 类 号：O322[理学—一般力学与力学基础]