Zeitschrift für verallgemeinerte Lügentheorie und -anwendungen

Multiscale Coordination Dynamics Topological Portraits

Abstract

William Kalie

On multiple spatiotemporal scales, living systems exhibit complex yet organised behaviour. To investigate the nature of multiscale coordination in living systems, a meaningful and systematic method of quantifying the complex dynamics is required, which is a challenge in both theoretical and empirical domains. The current work demonstrates how combining approaches from computational algebraic topology and dynamical systems can assist us in meeting this challenge. We concentrate on the application of multiscale topological analysis to coordinated rhythmic processes in particular. First, theoretical arguments are presented to demonstrate why certain topological features and their scale dependency are critical for comprehending complex collective dynamics. Second, we propose using persistent homology to capture such dynamically relevant topological information.