【作者】 秦志英； 陆启韶；

【Author】 QinZhiying1,2,LuQishao 1(1.School of Science,Beijing University ofAeronautics andAstronautics,Beijing 100083)(2.School of Mechanical and Electrical Engineering,Hebei University of Science and Technology,Shijiazhuang 050054)

【机构】 北京航空航天大学理学院； 河北科技大学机械电子工程学院；

【摘要】 本文从流分析的角度系统介绍了微分方程中的三类非光滑分岔,即擦边分岔、角点碰撞分岔、滑动分岔。通过非连续映射的推导,考虑全局Poincaré映射,得到了一个具有奇异性的分段线性-非线性规范形映射,不同的非光滑分岔对应不同奇异性。针对该规范形映射,对非光滑映射中特有的C-分岔进行了分析,发现映射的奇异性是以线性为界的,平方根奇异性和3/2奇异性的C-分岔有很大的不同。更多还原

【Abstract】 In this paper three kinds of nonsmooth bifurcations in differential equation are introduced from flow analysis,such as grazing bifurcation,corner-collision bifurcation and sliding bifurcation.The normal form map is a piecewise linear-nonlinear map with different singularity corresponding to different nonsmooth bifurcation,which can be derived by deducing discontinuous map and considering the global Poincarémap.By analyzing the typical C-bifurcation for the normal form map,it is found that the singularity is partitioned with linearity,and the C-bifurcation for square root and 3/2 singularity are different.更多还原