论文标题
欧拉（Eulerian
Toral CW complexes and bifurcation control in Eulerian flows with multiple Hopf singularities
论文作者
论文摘要
我们关注的是分叉分析和控制非谐波n-Tuple hopf奇异性的非线性欧拉流动。该分析与流动不变的Clifford Hypertori的CW复合物分叉有关，在其中我们指的是Toral CW复合物的这些折纸。我们观察到与两种最通用病例相关的单参数系统的初级到第三纪至三级流动性托拉尔CW复合分叉。在特定情况下，第三级CW复合物分叉并驻留在次级托拉尔CW复合物之外。当参数变化时，次级内部CW复合物与原点崩溃。但是，即使在二级内部歧管消失之后，第三级外部CW复合物仍继续生活。我们的分析始于状态空间的流动初级细胞分解。每个开放式细胞通过平滑的流动叶片均接受二级细胞分解。叶子的每个叶子都是对所有Eulerian流动的状态空间配置的最小流动不变性实现，并具有N-Tuple Hopf奇异性。允许的叶子矢量场保留转换是通过叶序列上非线性矢量场的Lie代数结构引入的。为单数叶流提供了完整的参数叶片正常形式分类。对三个与一到三个展开的分叉参数相关的最大叶子形式的叶片形式的叶片分析分析。叶出现品种得出。叶构型为不变的Toral CW复合物的细胞分类控制提供了一个场所。使用Maple实施和验证结果，用于对这种参数非线性振荡器的实际分叉控制。
We are concerned with bifurcation analysis and control of nonlinear Eulerian flows with non-resonant n-tuple Hopf singularity. The analysis is involved with CW complex bifurcations of flow-invariant Clifford hypertori, where we refer to these toral manifolds by toral CW complexes. We observe from primary to tertiary flow-invariant toral CW complex bifurcations for one-parametric systems associated with two most generic cases. In a particular case, a tertiary toral CW complex bifurcates from and resides outside a secondary toral CW complex. When the parameter varies, the secondary internal toral CW complex collapses with the origin. However, the tertiary external toral CW complex continues to live even after the secondary internal toral manifold disappears. Our analysis starts with a flow-invariant primary cell-decomposition of the state space. Each open cell admits a secondary cell-decomposition via a smooth flow-invariant foliation. Each leaf of the foliations is a minimal flow-invariant realization of the state space configuration for all Eulerian flows with n-tuple Hopf singularities. Permissible leaf-vector field preserving transformations are introduced via a Lie algebra structure for nonlinear vector fields on the leaf-manifold. Complete parametric leaf-normal form classification is provided for singular leaf-flows. Leaf-bifurcation analysis of leaf-normal forms are performed for three most leaf-generic cases associated with one to three unfolding bifurcation-parameters. Leaf-bifurcation varieties are derived. Leaf-bifurcations provides a venue for cell-bifurcation control of invariant toral CW complexes. The results are implemented and verified using Maple for practical bifurcation control of such parametric nonlinear oscillators.
