Self-Organised Critical Dynamics as a Key to Fundamental Features of Complexity in Physical, Biological, and Social Networks

Studies of many complex systems have revealed new collective behaviours that emerge through the mechanisms self-organised critical fluctuations. Subject to external and endogenous driving forces, these states with long-range spatial temporal correlations often arise from intrinsic dynamics threshold nonlinearity geometry-conditioned interactions. The self-similarity fluctuations enables us describe system using fewer parameters universal functions that, on other hand, can simplify computational information complexity. Currently, cutting-edge research across scales strives formulate a unifying mathematical framework, utilise properties in theory, decipher role hidden geometry. As prominent example, we study field-driven spin hysteresis loop network higher-order structures described by simplicial complexes, which provides geometric-frustration environment. While providing motivational illustrations physical, biological, social systems, along their networks, also demonstrate how criticality occurs at interplay topology mode. This opens up promising routes powerful tools address long-standing challenge theory applications complexity science ingrained efficient analysis under competing interactions embedded geometries.