| 一类自治离心式调速器系统的Hopf分岔与混沌 |
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| 引用本文： | 周良强,陈予恕,陈芳启.一类自治离心式调速器系统的Hopf分岔与混沌[J].机械强度,2012,34(2):165-169. |
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| 作者姓名： | 周良强 陈予恕 陈芳启 |
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| 作者单位： | 1. 南京航空航天大学理学院数学系,南京210016;天津市非线性动力学与混沌控制重点实验室,天津300072
2. 天津大学机械工程学院力学系,天津300072;天津市非线性动力学与混沌控制重点实验室,天津300072 |
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| 基金项目： | 国家自然科学基金(10972099,11172125);中国博士后基金(20110491419);南京航空航天大学青年科创基金(NS2012061)资助项目~~ |
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| 摘 要： | 研究一类自治离心式调速器系统的Hopf分岔与混沌运动等复杂动力学行为。利用Taylor级数展开得到离心调速器系统在平衡点附近的运动方程,并利用Hopf分岔定理研究系统发生Hopf分岔的条件及相应分岔解的稳定性,数值模拟验证理论分析结果。用4阶Runge-Kutta方法对这类自治系统进行计算,利用相图、Poincaré截面、分岔图等研究该系统的混沌运动。通过对系统参数的不断变化,分析得出系统由Hopf分岔通向混沌又进入周期运动的演化过程。
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| 关 键 词： | 调速器 Hopf分岔 周期运动 Poincaré截面 混沌 |
HOPF BIFURCATION AND CHAOS OF A CLASS OF AUTONOMOUS CENTRIFUGAL GOVERNOR SYSTEM |
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| ZHOU LiangQiang
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CHEN YuShu
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CHEN FangQi.HOPF BIFURCATION AND CHAOS OF A CLASS OF AUTONOMOUS CENTRIFUGAL GOVERNOR SYSTEM[J].Journal of Mechanical Strength,2012,34(2):165-169. |
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| Authors: | ZHOU LiangQiang CHEN YuShu CHEN FangQi |
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| Affiliation: | 1,3 (1.Department of Mathematics,Nanjing University of Aeronautics and Astronautics,Nanjing 210016,China)(2.Department of Mechanics,Tianjin University,Tianjin 300072,China)(3.Tianjin Key Laboratory of Nonlinear Dynamics and Chaos Control,Tianjin 300072,China) |
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| Abstract: | Complicated dynamical behaviors including Hopf bifurcation and chaotic motions of a class of autonomous centrifugal governor system are studied.By the Taylor’s series expansion,the equations of the centrifugal governor system near the equilibrium point are obtained.The conditions and stability of the Hopf bifurcation solution are obtained with Hopf bifurcation theory.Numerical simulations confirm the analytical results.Chaotic motions of this system are also investigated by using the phase portraits,Poincaré sections and bifurcation diagrams.The evolution through Hopf bifurcation to chaos,and then to periodic motions again is shown by the bifurcation diagrams under different sets of system parameters. |
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| Keywords: | Centrifugal governor Hopf bifurcation Periodic motion Poincaré section Chaos |
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