An information-theoretic approach to self-organisation: Emergence of complex interdependencies in coupled dynamical systems

Abstract

Self-organisation lies at the core of fundamental but still unresolved scientific questions, and holds the promise of de-centralised paradigms crucial for future technological developments. While self-organising processes have been traditionally explained by the tendency of dynamical systems to evolve towards specific configurations, or attractors, we see self-organisation as a consequence of the interdependencies that those attractors induce. Building on this intuition, in this work we develop a theoretical framework for understanding and quantifying self-organisation based on coupled dynamical systems and multivariate information theory. We propose a metric of global structural strength that identifies when self-organisation appears, and a multi-layered decomposition that explains the emergent structure in terms of redundant and synergistic interdependencies. We illustrate our framework on elementary cellular automata, showing how it can detect and characterise the emergence of complex structures.

arXiv comment25 pages, 4 figures

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• Integrated information as a common signature of dynamical and information-processing complexity
• An operational information decomposition via synergistic disclosure
• Functional Connectome of the Human Brain with Total Correlation
• Generalised Measures of Multivariate Information Content
• A generalization of the maximum entropy principle for curved statistical manifolds
• An information-theoretic approach to hypergraph psychometrics