论文标题
平面分段线性差异系统中的马鞍节雀快周期
Saddle-node canard cycles in planar piecewise linear differential systems
论文作者
论文摘要
通过采用奇异的扰动方法，分析了一个奇异扰动的平面分段线性（PWL）差异系统所表现出的CANARD极限周期。进行的研究涉及在超临界和亚临界型霍夫夫分叉后出现的双曲线和非纤维罐头限制周期。 获得的结果与平滑矢量场获得的结果完全可比。从某种意义上说，手稿可以理解为对Krupa和Szmolyan [18]获得平滑系统的PWL框架的扩展。此外，还获得了一些新型的缓慢快速行为。特别是在超临界情况下，在适当的条件下，证明极限周期是沿着表现出两个折叠的曲线组织的。这些褶皱中的每一个都对应于牛排限制周期的鞍节点分叉，一个涉及无头牛排循环，而另一个涉及带有头部的牛排周期。这种配置允许共存三个CANARD限制周期。
By applying a singular perturbation approach, canard limit cycles exhibited by a general family of singularly perturbed planar piecewise linear (PWL) differential systems are analyzed. The performed study involves both hyperbolic and non-hyperbolic canard limit cycles appearing after both a supercritical and a subcritical Hopf bifurcation. The obtained results are completely comparable with those obtained for smooth vector fields. In some sense, the manuscript can be understood as an extension towards the PWL framework of the results obtained for smooth systems by Krupa and Szmolyan [18]. In addition, some novel slow-fast behaviors are obtained. In particular, in the supercritical case, and under suitable conditions, it is proved that the limit cycles are organized along a curve exhibiting two folds. Each of these folds corresponds to a saddle-node bifurcation of canard limit cycles, one involving headless canard cycles, whereas the other involving canard cycles with head. This configuration allows the coexistence of three canard limit cycles.
