SD振子,SD吸引子及其应用  

SD oscillator,the attractor and their applications

作　　者：曹庆杰[1] Wiercigroch M Pavlovskaia E E Grebogi C Thompson M T 

机构地区：[1]石家庄铁道学院数理系,河北石家庄050043 [2]Centre for Applied Dynamics Research,Department of Engineering,University of Aberdeen,King's College,Aberdeen AB24 3UE,Scotland,UK

出　　处：《振动工程学报》2007年第5期454-458,共5页Journal of Vibration Engineering

摘　　要：提供一个新振子命名为SD振子,受扰振子的吸引子称为SD吸引子,它的动力学行为决定于一个光滑参数α的连续变化。这是一个具有强非线性特征的振动系统,它提供了一个从光滑动力学行为向不连续动力学行为光滑转迁的典型示范,这种直接的转迁并不需要连续系统的过渡。当系统为光滑动力学性态时,表现出与Du ffing系统类似的双井等标准动力学行为,而当系统表现为不连续性态时,提供一个新的非连续动力系统模型,它除了表现为标准的双井动力学行为外,也表现出一些新的非标准动力学行为。文中展示了这个系统的转迁过程和特性及其相应的吸引子的复杂动力学行为。A new oscillator which is named SD oscillator is proposed. The perturbed attractors are called SD attractors. The dynamics of this oscillator depend on the smooth varying for a smooth parameter α. This oscillator is of strong non-linearity providing an example of transient from smooth dynamics to the one of discontinuity. The standard dynamics of double-well can be seen for the smooth system, which is similar with Dulling system. In addition to the standard dynamics, the discontin- uous system behaves non-standard dynamics which is known as the saddle-like singularity and homoclinic-like orbit.

关 键 词：SD吸引力 LYAPUNOV指数 类鞍点 类同宿轨道 

分 类 号：O322[理学—一般力学与力学基础]