Sequences by Metastable Attractors: Interweaving Dynamical Systems and Experimental Data

Frontiers in Applied Mathematics and Statistics

Hutt, Axel¹  beim Graben, Peter² 

[1] Department of Data Assimilation, German Weather Service, Offenbach, Germany;Department of Mathematics, University of Reading, Reading, United Kingdom

关键词: Recurrence structure analysis;    Event-Related Brain Potentials;    Metastability;    neural fields;    Kernel construction;    heteroclinic sequences;   

DOI  :  10.3389/fams.2017.00011

学科分类：数学（综合）

来源: Frontiers

【 摘 要 】

Metastable attractors and heteroclinic orbits are present in the dynamics of various complex systems. Although their occurrence is well-known, their identification and modeling is a challenging task. The present work reviews briefly the literature and proposes a novel combination of their identification in experimental data and their modeling by dynamical systems. This combination applies recurrence structure analysis permitting the derivation of an optimal symbolic representation of metastable states and their dynamical transitions. To derive heteroclinic sequences of metastable attractors in various experimental conditions, the work introduces a Hausdorff clustering algorithm for symbolic dynamics. The application to brain signals (event-related potentials) utilizing neural field models illustrates the methodology.

【 授权许可】

CC BY