AUTHOR=Hutt Axel , beim Graben Peter TITLE=Sequences by Metastable Attractors: Interweaving Dynamical Systems and Experimental Data JOURNAL=Frontiers in Applied Mathematics and Statistics VOLUME=3 YEAR=2017 URL=https://www.frontiersin.org/journals/applied-mathematics-and-statistics/articles/10.3389/fams.2017.00011 DOI=10.3389/fams.2017.00011 ISSN=2297-4687 ABSTRACT=

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.