余维-1非光滑分岔下的簇发振荡及其机理
发布时间：2019-07-20 19:49
【摘要】：不同尺度耦合会导致一些特殊的振荡行为,通常表现为大幅振荡与微幅振荡的组合,也即所谓的簇发振荡.迄今为止,相关工作大都是围绕光滑系统开展的,而非光滑系统中由于存在着各种形式的非常规分岔,从而可能会导致更为复杂的簇发振荡模式.本文旨在揭示存在非光滑分岔时动力系统的不同尺度耦合效应.以典型的含两个非光滑分界面的广义蔡氏电路为例,通过引入周期变化的电流源以及一个用于控制的电容,选取适当的参数使得周期频率与系统频率之间存在量级差距,建立了含不同尺度的四维分段线性动力系统模型.基于快子系统在不同区域中的平衡点及其稳定性分析,以及系统轨迹穿越非光滑分界面时的分岔分析,得到了不同余维非光滑分岔的存在条件及其分岔行为.重点探讨了余维-1非光滑分岔下的簇发振荡的吸引子结构及其产生机理,揭示了非光滑分岔下系统复杂振荡行为的本质.
[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.
【作者单位】： 江苏大学理学院;
【基金】：国家自然科学基金(批准号:11472115,11472116) 江苏省青蓝工程资助的课题~~
【分类号】：O19
本文编号：2516887
[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.
【作者单位】： 江苏大学理学院;
【基金】：国家自然科学基金(批准号:11472115,11472116) 江苏省青蓝工程资助的课题~~
【分类号】：O19
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1 张正娣;毕勤胜;;非光滑动力系统中的不同尺度效应及其分岔机制[A];第六届全国动力学与控制青年学者学术研讨会论文摘要集[C];2012年
，本文编号：2516887
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