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Abstract:
Hermann Haken’s synergetics provides a fundamental theoretical framework for understanding the emergence of macroscopic order from microscopic interactions in complex dynamical systems. In this paper, we explore how different ways of quantifying recurrences serve as powerful tools to analyse phase-space dynamics within this synergetic perspective. Recurrence-based methods uncover evolving patterns, transitions between regular and chaotic behaviour, and characteristic time-scale separations that govern complex dynamics. We further discuss recent advances in combining recurrence analysis with machine learning, highlighting their potential to uncover hidden dynamical patterns and inform predictive modelling. Overall, recurrence approaches can be regarded as a synergetically motivated avenue for studying the universal properties of non-linear systems across disciplines.
