Lattice Structures for Attractors II
Lattice Structures for Attractors II
复制标题
吸引子 II 的晶格结构
DOI：
10.1007/s10208-015-9272-x
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发表时间：
2013
影响因子：
3
通讯作者：
R. Vandervorst
中科院分区：
文献类型：
--
作者：
W. Kalies;K. Mischaikow;R. Vandervorst
动力系统中吸引子的代数结构决定了它的大部分全局动力学性质。所有吸引子的集合具有自然的晶格结构，并且这种结构可以通过吸引邻域来检测，原则上可以计算。事实上，最近已经有很多关于开发和实现全局动力学的通用计算算法的工作，这些算法能够有效地计算吸引邻域。在这里，我们解决的问题，是否所有的代数结构的吸引子可以捕获这些方法。
The algebraic structure of the attractors in a dynamical system determines much of its global dynamics. The collection of all attractors has a natural lattice structure, and this structure can be detected through attracting neighborhoods, which can in principle be computed. Indeed, there has been much recent work on developing and implementing general computational algorithms for global dynamics, which are capable of computing attracting neighborhoods efficiently. Here we address the question of whether all of the algebraic structure of attractors can be captured by these methods.