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光滑系统
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  differential system
    The weak differential system and the maximum principle
    弱光滑系统与最大值原理
短句来源
    The weak differential system and the optimal control problems
    弱光滑系统的最优控制理论
短句来源
    ResultsThe maximum principle on the optimal control of weaker differential system is researched.
    结果 得到了弱光滑系统最优控制的最大值原理。
短句来源
  continuum system
    Catastrophe theory can effectively solve catastrophe problem that can possible appear in continuum system.
    突变理论能比较有效地解决光滑系统中可能出现的突变问题。
短句来源
  “光滑系统”译为未确定词的双语例句
    Matrosov Stability Theorems for a Class of Nonautonomous and Nonsmooth Switched System
    非自治非光滑系统的Matrosov稳定性定理
短句来源
    In chapter 6, with the results of above chapters, we discuss the optimal control problems for weak-smooth system and draw a conclusion coinciding with that of smooth system, i.e., the Pontryagin's maximum principle (see Th 6.2.7).
    第六章,在以上各章结果的基础上,研究了弱光滑系统的最优控制问题,得到了与光滑系统一致的结果——庞特李雅金类型的最大值原理(即定理6.2.7)。
短句来源
    around the bifercation point of the doubling period from period 1 to period 2,the orbit of period 2 is not perpendsculor to the path of period 1, and the chaos is reached by jumping from orbit 6 directly.
    例如,与光滑系统中典型的倍周期分岔不同的是,在周期1到周期2的倍周期分岔点附近,周期2轨道分枝不垂直于周期1轨道分枝,并且直接经周期6到达混沌态.
短句来源
    Border collision bifurcations and chaos in a class of piecewise smooth systems with two boundaries
    一类具有两个边界的分段光滑系统中边界碰撞分岔现象及混沌
短句来源
    Chaotic Attractor in a Piecewise-Smooth System
    一个分段光滑系统中的混沌吸引子
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  differential system
Global existence for a semilinear differential system
      
One allows the appearance of eight limit cycles in the neighborhood of infinity, which is the first example that a polynomial differential system bifurcates eight limit cycles at infinity.
      
Certain Ergodic Properties of a Differential System on a Compact Differentiable Manifold
      
Let Mn be an n-dimensional compact C∞-differentiable manifold, n ≥ 2, and let S be a C1-differential system on Mn.
      
Filtration of a random process in a statistically uncertain linear stochastic differential system
      
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In this paper we present the analytic expressions of partition lines in the parametric space of a piece\|wise smooth mapping describing an electronic relaxation oscillator. The supercritical regions with permission of period\|doubling bifurcation, prohibition of period\|doubling bifurcation, and complete phase\|locking are discussed. Among them the region, where period\|doubling bifurcation is prohibited but chaos is permitted is reported for the first time to our knowledge. These kinds of phenomena and regions...

In this paper we present the analytic expressions of partition lines in the parametric space of a piece\|wise smooth mapping describing an electronic relaxation oscillator. The supercritical regions with permission of period\|doubling bifurcation, prohibition of period\|doubling bifurcation, and complete phase\|locking are discussed. Among them the region, where period\|doubling bifurcation is prohibited but chaos is permitted is reported for the first time to our knowledge. These kinds of phenomena and regions can be observed in a lot of similar systems.

解析导出了描述一种电子张弛振子的分段光滑圆映象在参数空间超临界区域内显示几种不同动力学行为的子区域分界线.这些子区域分别是:允许倍周期分岔发生的区域,禁止倍周期分岔发生的区域,以及完全锁相区域.类似的现象和子区域可以在许多分段光滑系统中观察到

This paper deals with rub impacts of a rotor system with elastic case by using the method of Poincaré map. Two kinds of Poincaré map are constructed in order to study different characters of rub impacting motions, including the numbers of period and impact. It is found that the non smooth feature of piecewise smooth vector fields is very rich and complex. The rub impacting motions of the system are mainly chaotic, but periodic motions ...

This paper deals with rub impacts of a rotor system with elastic case by using the method of Poincaré map. Two kinds of Poincaré map are constructed in order to study different characters of rub impacting motions, including the numbers of period and impact. It is found that the non smooth feature of piecewise smooth vector fields is very rich and complex. The rub impacting motions of the system are mainly chaotic, but periodic motions are also possible for parameters properly chosen, and various period windows are embedded in the chaotic region. The bifurcating rule of the system with the variation of case stiffness is also obtained through numerical simulations. It is shown that the rub impacts of the rotor system become even voilent as the case stiffness increases. As a special and simplified model, a constrained differential system describing rigid impacts of rotor systems are studied and some new results are shown.

分别采用两种不同的截面建立 Poincaré映射 ,对转子 -弹性机壳系统的碰摩运动进行了研究 ,得到了该类分段光滑系统运动的一般特点和转子碰摩运动随碰撞刚度变化发生分岔的规律。研究表明 ,该系统的碰摩运动主要以混沌形式出现 ,但不同的周期窗口按一定规律嵌入混沌区内。随着定子碰撞刚度增加 ,碰摩运动将会加剧。然后由该系统导出了刚性转子碰摩的约束微分系统 ,从而将碰摩转子系统的两种不同描述形式统一起来 ,并分析了周期刚性碰摩运动的分岔情况

In this paper, we introduce a weaker differential system that includes many control systems as special cases, and discuss the optimal control problem relevant to the system.

提出了弱光滑系统概念 ,并讨论了与之相关的最优控制问题 .

 
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