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Conley Index Approach to Sampled Dynamics
SIAM Journal on Applied Dynamical Systems ( IF 2.1 ) Pub Date : 2020-03-30 , DOI: 10.1137/19m1254404 Bogdan Batko 1 , Konstantin Mischaikow 2 , Marian Mrozek 1 , Mateusz Przybylski 1
SIAM Journal on Applied Dynamical Systems ( IF 2.1 ) Pub Date : 2020-03-30 , DOI: 10.1137/19m1254404 Bogdan Batko 1 , Konstantin Mischaikow 2 , Marian Mrozek 1 , Mateusz Przybylski 1
Affiliation
SIAM Journal on Applied Dynamical Systems, Volume 19, Issue 1, Page 665-704, January 2020.
The topological method for the reconstruction of dynamics from time series [K. Mischaikow et al., Phys. Rev. Lett., 82 (1999), pp. 1144--1147] is reshaped to improve its range of applicability, particularly in the presence of sparse data and strong expansion. The improvement is based on a multivalued map representation of the data. However, unlike the previous approach, it is not required that the representation has a continuous selector. Instead of a selector, a recently developed new version of Conley index theory for multivalued maps [B. Batko, SIAM J. Appl. Dyn. Syst., 16 (2017), pp. 1587--1617; B. Batko and M. Mrozek, SIAM J. Appl. Dyn. Syst., 15 (2016), pp. 1143--1162] is used in computations. The existence of a continuous, single valued generator of the relevant dynamics is guaranteed in the vicinity of the graph of the multivalued map constructed from data. Some numerical examples based on time series derived from the iteration of Hénon-type maps are presented.
中文翻译：
采样动力学的康利指数方法
SIAM Journal on Applied Dynamical Systems，第 19 卷，第 1 期，第 665-704 页，2020 年 1 月。
从时间序列重建动力学的拓扑方法[K. Mischaikow 等人，物理学。Rev. Lett., 82 (1999), pp. 1144--1147] 被重塑以提高其适用范围，特别是在存在稀疏数据和强扩展的情况下。改进基于数据的多值地图表示。但是，与之前的方法不同，表示不需要具有连续选择器。不是选择器，而是最近开发的用于多值映射的康利指数理论的新版本 [B. Batko, SIAM J. Appl. 达因。系统，16 (2017)，第 1587--1617 页；B. Batko 和 M. Mrozek，SIAM J. Appl。达因。Syst., 15 (2016), pp. 1143--1162] 用于计算。连续存在，相关动态的单值生成器在由数据构建的多值图的图形附近得到保证。介绍了一些基于时间序列的数值示例，这些时间序列源自 Hénon 型地图的迭代。
更新日期：2020-03-30
The topological method for the reconstruction of dynamics from time series [K. Mischaikow et al., Phys. Rev. Lett., 82 (1999), pp. 1144--1147] is reshaped to improve its range of applicability, particularly in the presence of sparse data and strong expansion. The improvement is based on a multivalued map representation of the data. However, unlike the previous approach, it is not required that the representation has a continuous selector. Instead of a selector, a recently developed new version of Conley index theory for multivalued maps [B. Batko, SIAM J. Appl. Dyn. Syst., 16 (2017), pp. 1587--1617; B. Batko and M. Mrozek, SIAM J. Appl. Dyn. Syst., 15 (2016), pp. 1143--1162] is used in computations. The existence of a continuous, single valued generator of the relevant dynamics is guaranteed in the vicinity of the graph of the multivalued map constructed from data. Some numerical examples based on time series derived from the iteration of Hénon-type maps are presented.
中文翻译：
采样动力学的康利指数方法
SIAM Journal on Applied Dynamical Systems，第 19 卷，第 1 期，第 665-704 页，2020 年 1 月。
从时间序列重建动力学的拓扑方法[K. Mischaikow 等人，物理学。Rev. Lett., 82 (1999), pp. 1144--1147] 被重塑以提高其适用范围，特别是在存在稀疏数据和强扩展的情况下。改进基于数据的多值地图表示。但是，与之前的方法不同，表示不需要具有连续选择器。不是选择器，而是最近开发的用于多值映射的康利指数理论的新版本 [B. Batko, SIAM J. Appl. 达因。系统，16 (2017)，第 1587--1617 页；B. Batko 和 M. Mrozek，SIAM J. Appl。达因。Syst., 15 (2016), pp. 1143--1162] 用于计算。连续存在，相关动态的单值生成器在由数据构建的多值图的图形附近得到保证。介绍了一些基于时间序列的数值示例，这些时间序列源自 Hénon 型地图的迭代。
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