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中文摘要：
研究了受外部扰动的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,建立了离心调速器系统的动力学方程,通过Lyapunov指数研究了系统的超混沌行为,通过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指数谱是完全吻合的.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混合投影同步,数值仿真进一步验证了该控制方案的有效性.
英文摘要：
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 characteristics 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.
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