三时间尺度下非光滑电路中的簇发振荡及机理

实际工程应用中存在着诸如冲击、干摩擦、切换等非光滑因素,以此建立的动力学模型是包含非光滑项的系统.目前针对非光滑动力系统的研究大多基于单一尺度或者两尺度,而含有更多尺度的非光滑动力系统可能会存在更复杂的动力学现象.本论文旨在探讨非光滑动力系统中的多尺度效应及其分岔机制.基于典型的非光滑蔡氏电路,引入一个与系统固有频率存...

BURSTING OSCILLATIONS AND ITS MECHANISM IN A NONSMOOTH SYSTEM WITH THREE TIME SCALES

Dynamic models established from practical engineering application are non-smooth systems owing to non-smooth factors, such as impact, dry friction and switching, etc. Up to now, most studies are in terms of the non-smooth dynamic systems with a single scale or two scales. While more complex dynamic phenomena may be observed in the non-smooth dynamic systems with more scales. The main purpose of this work is to explore multiscale effect in a non-smooth electric system and the related bifurcation mechanism. Upon the traditional Chua's circuit, by introducing a periodically excited oscillator with an order gap from the natural frequency of the system and taking suitable parameter values, a coupled 4-dimensional piecewise linear dynamic system with three time-scales and two boundaries is established to study the bursting oscillations as well as the corresponding bifurcation mechanism under three time-scales. Merging the variables corresponding to the fast scale and the variables related to the intermediate scale into the fast variables, while regarding the variable corresponding to the slow scale as the slow variable, the coupled problem with three time-scales is transformed into that with two time-scales. According to the relevant Hopf bifurcation curve under two independent parameters and the stability analyses of the slow submanifold of the fast subsystem, two different bursting oscillations of the coupled dynamic system are given in the case of two different parameter values. On the basis of the fast-slow analysis method, the transformed phase portrait and the non-smooth dynamics of the slow submanifold occurring on the non-smooth boundaries, the bifurcation mechanism of the mutual transformation of different bursting oscillations is analyzed in details, in which some helpful numerical simulations are given to illustrate the validity of our study simultaneously. At the same time, a new evolution of bursting oscillations is found, i.e., the bursting oscillation induced by destructive grazing bifurcation.