SD振子的非线性动力学特征研究

Investigations of Nonlinear Dynamics for SD Oscillator

介绍了SD振子的非线性动力学行为。该振子是一个具有强非线性特征的振动系统,其动力学行为决定于一个光滑参数α的连续变化,当参数α>0时,系统为光滑的,而当参数α=0时,系统为不连续的。SD振子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范例。当系统为光滑时,表现出与Duffing系统类似的标准双阱动力学行为;当系统表现为不连续时,除表现为非标准的双阱动力学行为外,同时具有如类鞍点和类同宿轨道等非标准动力学行为。还给出一个刚性耦合的SD振子,该振子具有单阱、双阱、三阱动力学特征及随参数变化由光滑动力学行为向不连续动力学行为的转迁特性。

In this paper, we introduce the nonlinear dynamics of the recently proposed SD oscillator, which behaves both smooth and discontinuous dynamics with strong nonlinearity. The dynamics of this oscillator depends on a smooth varying parameter α. If a 〉 0 the system is smooth behaving standard dynamics with double well potential while when α= 0 it is discontinuous admitting a nonstandard dynamics with homoclinic-like double well potential and a saddle-like singularity. We also propose a rig coupled SD oscillator which exhibits both standard and nonstandard nonlinear behavior with single, double and triple well potential and the transition as parameter changes.