一类具鞍点-可视折点的平面Filippov系统的分支分析
Bifurcation Analysis for a Class of Planar Filippov Systems with Saddle-Visible Fold Singularity
DOI: 10.12677/AAM.2024.134114, PDF,   
作者: 陈艺琳：长沙理工大学数学与统计学院, 湖南 长沙
关键词: Filippov系统；鞍点-可视折点；规范型；分支；Filippov System； Saddle-Visible Fold Singularity； Normal Form； Bifurcation
摘要: 本文研究了具有余维 2 鞍点-可视折点的平面 Filippov 系统的一般展开. 首先, 利用规范型及滑模 动力学, 完整地给出了分岔图. 其次, 证明了鞍点-可视折点附近存在伪边界鞍点分支和两个可视折 点的碰撞 V V1 分支. 特别地, 我们还证明了在 β1 < 0 的参数空间中存在两条余维 1 分支曲线. 最 后, 我们的结果表明某些特殊分段线性微分系统的鞍点-可视折点的分支现象也适用于一般的平面 Filippov 系统.
Abstract: In this paper, we investigate the generic unfolding of planar Filippov systems with codimension-2 saddle-visible fold singularity. Firstly, the bifurcation diagrams are given completely by means of normal forms and sliding mode dynamics. Secondly, it is proved that there are pseudo boundary saddle bifurcation and collisions of visible two-fold singularity V V1 bifurcation near saddle-visible fold singularity. In particular, we shown that there exist two codimension-1 bifurcation curves in the parameter space of β1 < 0. Finally, our results indicate the saddle-visible fold singularity branching phenomenon in some special piecewise linear differential systems also hold for general planar Filippov systems.
文章引用：陈艺琳. 一类具鞍点-可视折点的平面Filippov系统的分支分析[J]. 应用数学进展, 2024, 13(4): 1234-1247. https://doi.org/10.12677/AAM.2024.134114

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