In this dissertation , we study some stability properties for two impulsive differential systems employing lyapunov ' s second method : one system is impulsive hybrid differential system : the other is differertial system with impulses at variable time : herein these stability results do not require a lyapunov function to have a negative definite first derivative along trajectories of the system , further we may not require its derivative to restrict the function increasing growth ; and we do not give conditions on continuous portion or discrete portion of the systems respective ! } " , hence we can give mixing conditions on them 在这篇硕士学位论文中，我们主要借助lyapunov第二方法的思想，讨论了两类脉冲微分系统：脉冲混合微分系统和具有依赖于状态脉冲的微分系统的稳定性问题。不同于以往的研究，本文所找的lyapunov函数沿系统轨线的一阶导数不再局限于常负或定负，甚至不用其导数来限制其增长速度；不再局限于对离散或连续部分分别设置条件，而是对其离散和连续部分设置混合条件。
It is constructed that radial impact and rubbing dynamics differential equations of the rotor system having the nonlinear rigidity on the unsteady and non - linear oil film . the bifurcation and chaos behavior of impact and rubbing fault rotor system caused by the parameters of nonlinear rigidity , rotor rotating speed , eccentric mass is analyzed , in the numerical value analysis method . the bifurcation diagrams , maximum lyapunov exponent diagrams , poincar maps , phase plane portraits , trajectories of journal center , time - history curve , amplitude spectra diagrams of the rotor motion are used ( 2 )建立了具有非线性刚度的转子系统在非稳态非线性油膜力作用下的径向碰摩动力学微分方程,并应用含高阶余项的非线性动力方程的线性化数值法研究了此类系统响应的复杂动力学行为,利用转子响应的分岔图、最大lyapunov指数曲线、 poincar截面映射、时域波形、相轨线、轴心轨迹、幅值谱等图形分析了系统响应的周期运动、拟周期运动、倍周期分岔、混沌等运动形式的转化与演变过程,重点研究了非线性刚度、转子转速、偏心质量等系统参数对碰摩故障转子系统的分岔和混沌行为的影响。
Especially , when the isocline of x is monotone decreasing in 0 < x < 1 , the svstem has no limit cycle and is globally stable ; next , we construct a saddle bifurcation at the boundary equilibrium and a degenerated bogdanov - takens bifurcation at the interior equilibrium by choosing appropriate parameter values in the following two sections , where our work are based on the theory of central manifolds and normal torms . we prove that is a codimention 3 focus - type equilibrium . system ( 6 . 1 ) will have two limit cycles at some appropriate bifurcation parameter values , and have homoclinic or double - homoclinic orbits at some other appropriate bifurcation parameter values ; at last , we study the qualitative properties of the system at infinite in the poincare sphere 因为系统在( 0 ， 0 )点处没有定义，这给研究其在( 0 ， 0 )附近的动力学性质带来了困难，我们应用文献[ 17 ]中关于研究非线性方程奇点的系列理论和方法，圆满解决了这一问题，给出了第一象限内当t +或t -时，在全参数状态下系统的轨线趋于( 0 ， 0 )点的所有可能情况，其相图也得以描绘；并且，系统不存在极限环的几个充分条件我们也予以列出，当x的等倾线在0 x 1范围内递减时，系统不存在极限环，全局渐近稳定；然后，我们以中心流形定理和正规型方法为主要工具，巧妙选择参数，分别构造了一个余维2的鞍点分岔和一个余维3退化bogdanov - takens分岔，证明了平衡点是余维3的焦点型平衡点，存在参数， m ，的值使得系统( 6 . 1 )有两个极限环，还存在参数， m ，的另外值使得系统( 6 . 1 )有同宿轨或双同宿轨。
