【摘要】：不同尺度耦合會導(dǎo)致一些特殊的振蕩行為,通常表現(xiàn)為大幅振蕩與微幅振蕩的組合,也即所謂的簇發(fā)振蕩.迄今為止,相關(guān)工作大都是圍繞光滑系統(tǒng)開展的,而非光滑系統(tǒng)中由于存在著各種形式的非常規(guī)分岔,從而可能會導(dǎo)致更為復(fù)雜的簇發(fā)振蕩模式.本文旨在揭示存在非光滑分岔時動力系統(tǒng)的不同尺度耦合效應(yīng).以典型的含兩個非光滑分界面的廣義蔡氏電路為例,通過引入周期變化的電流源以及一個用于控制的電容,選取適當(dāng)?shù)膮?shù)使得周期頻率與系統(tǒng)頻率之間存在量級差距,建立了含不同尺度的四維分段線性動力系統(tǒng)模型.基于快子系統(tǒng)在不同區(qū)域中的平衡點及其穩(wěn)定性分析,以及系統(tǒng)軌跡穿越非光滑分界面時的分岔分析,得到了不同余維非光滑分岔的存在條件及其分岔行為.重點探討了余維-1非光滑分岔下的簇發(fā)振蕩的吸引子結(jié)構(gòu)及其產(chǎn)生機理,揭示了非光滑分岔下系統(tǒng)復(fù)雜振蕩行為的本質(zhì).
[Abstract]:The coupling of different scales will lead to some special oscillations, which are usually the combination of large oscillations and microoscillations, that is, the so-called cluster oscillations. Up to now, most of the related work has been carried out around smooth systems, but there are various forms of unconventional bifurcation in non-smooth systems, which may lead to more complex cluster oscillations. The purpose of this paper is to reveal the coupling effects of dynamic systems with nonsmooth bifurcation at different scales. Taking the typical generalized Chua's circuit with two nonsmooth interfaces as an example, a four-dimensional piecewise linear dynamic system model with different scales is established by introducing a periodic current source and a capacitance for control, and selecting appropriate parameters to make an order of magnitude difference between the periodic frequency and the system frequency. Based on the equilibrium point and stability analysis of the fast subsystem in different regions, as well as the bifurcation analysis of the system trajectory passing through the nonsmooth bifurcation interface, the existence conditions and bifurcation behavior of the nonsmooth bifurcation with different codimensions are obtained. The Attractor structure and its generation mechanism of cluster oscillations under codimension-1 nonsmooth bifurcation are discussed in detail, and the essence of complex oscillatory behavior of the system under nonsmooth bifurcation is revealed.
【作者單位】： 江蘇大學(xué)理學(xué)院;
【基金】：國家自然科學(xué)基金(批準號:11472115,11472116) 江蘇省青藍工程資助的課題~~
【分類號】：O19

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1 張正娣;畢勤勝;;非光滑動力系統(tǒng)中的不同尺度效應(yīng)及其分岔機制[A];第六屆全國動力學(xué)與控制青年學(xué)者學(xué)術(shù)研討會論文摘要集[C];2012年

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本文編號：2516887