二维和三维动力系统吸引盆地分界线的图形表示
Graphical representation of separatrices of attraction basins in two and three dimensional dynamical systems
AI总结：
本文研究了动力系统中分界线的重建问题，通过构建算法检测并细化分界线流形上的点，利用无网格方法在二维和三维模型中实现分界线的重建。
摘要：
在本文中，我们考虑了动力系统中分界线的重建问题。特别是，我们旨在将领域划分，以近似不同稳定平衡点的吸引盆地的边界。我们从\cite{cavoretto11}中描述的二维情况以及\cite{cavoretto11,C-D-P-V}中提出的近似方案出发，然后扩展了在具有两个和三个稳定平衡点的三维模型中的分界线重建方案。为此，我们构建了用于检测和细化分界线流形上点的计算算法和程序。所采用的无网格方法用于重建分界线。
英文摘要：
In this paper we consider the problem of reconstructing separatrices in dynamical systems. In particular, here we aim at partitioning the domain approximating the boundaries of the basins of attraction of different stable equilibria. We start from the 2D case sketched in \cite{cavoretto11} and the approximation scheme presented in \cite{cavoretto11,C-D-P-V}, and then we extend the reconstruction scheme of separatrices in the cases of three dimensional models with two and three stable equilibria. For this purpose we construct computational algorithms and procedures for the detection and the refinement of points located on the separatrix manifolds that partition the phase space. The use of the so-called meshfree or meshless methods is used to reconstruct the separatrices.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
