摘要
SD振子及SD吸引子的动力学行为决定于一个光滑参数α的连续变化。当α>0时,系统表现为光滑特征;当α=0时,系统表现为不连续特性。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Duffing系统类似的双井等标准动力学行为;当系统表现为不连续性态时,除表现为标准的双井动力学行为外,也表现出如类鞍点和类同宿轨道等非标准动力学行为,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。
In this paper a new oscillator named the SD oscillator is proposed. The perturbed attractors are called the SD attractors, The dynamics of this oscillator depends on the smooth transition of a smooth parameter α. The oscillator behaves smoothly if the parameter α is greater than zero and it behaves with discontinuity if α=0. This oscillator is of strong non-linearity and serves as an example of transition from smooth dynamics to that of discontinuity. The standard dynamics of double-well can be seen as a smooth system, similar to Duffing system. In addition to the standard dynamics, the discontinuous system behaves as non-standard dynamics, with so-called the saddle-like singularity and homoclinic-like orbit.
出处
《科技导报》
CAS
CSCD
2007年第23期33-37,共5页
Science & Technology Review
基金
石家庄铁道学院重点课题资助项目(811025)
