Canonical Discontinuous Planar Piecewise Linear Systems
Canonical Discontinuous Planar Piecewise Linear Systems
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DOI：
10.1137/11083928x
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发表时间：
2012-01
期刊：
影响因子：
--
通讯作者：
E. Freire;E. Ponce;F. Torres
中科院分区：
文献类型：
--
作者：
E. Freire;E. Ponce;F. Torres
研究了一类由两个半平面非连续分段线性系统构成的Filippov系统族。在滑动集有界的一般条件下，通过改变变量和参数，得到了一个具有七个参数的类Lienard标准形。如果把注意力限制在滑动集上没有点的轨道上，这个标准型在拓扑上等价于原系统。在焦点-焦点动力学的假设下，得到了一个只有五个参数的简化标准形。对于没有平衡的情况下，在两个开放的半平面，我们描述了定性不同的相图，可以发生在参数空间和分叉连接它们。特别是，我们证明了可能存在两个极限环周围的滑动集。这样的极限环分叉在某些参数曲线，围绕不同的余维二Hopf分叉点组织。《Canonic》的…
The family of Filippov systems constituted by planar discontinuous piecewise linear systems with two half-plane linearity zones is considered. Under generic conditions that amount to the boundedness of the sliding set, some changes of variables and parameters are used to obtain a Lienard-like canonical form with seven parameters. This canonical form is topologically equivalent to the original system if one restricts one's attention to orbits with no points in the sliding set. Under the assumption of focus-focus dynamics, a reduced canonical form with only five parameters is obtained. For the case without equilibria in both open half-planes we describe the qualitatively different phase portraits that can occur in the parameter space and the bifurcations connecting them. In particular, we show the possible existence of two limit cycles surrounding the sliding set. Such limit cycles bifurcate at certain parameter curves, organized around different codimension-two Hopf bifurcation points. The proposed canonic...