Abstract
Studies of many complex systems have revealed new collective behaviours that emerge through the mechanisms of self-organised critical fluctuations. Subject to the external and endogenous driving forces, these collective states with long-range spatial and temporal correlations often arise from the intrinsic dynamics with the threshold nonlinearity and geometry-conditioned interactions. The self-similarity of critical fluctuations enables us to describe the system using fewer parameters and universal functions that, on the other hand, can simplify the computational and information complexity. Currently, the cutting-edge research on self-organised critical systems across the scales strives to formulate a unifying mathematical framework, utilise the critical universal properties in information theory, and decipher the role of hidden geometry. As a prominent example, we study the field-driven spin dynamics on the hysteresis loop in a network with higher-order structures described by simplicial complexes, which provides a geometric-frustration environment. While providing motivational illustrations from physical, biological, and social systems, along with their networks, we also demonstrate how the self-organised criticality occurs at the interplay of the complex topology and driving mode. This study opens up new promising routes with powerful tools to address a long-standing challenge in the theory and applications of complexity science ingrained in the efficient analysis of self-organised critical states under the competing higher-order interactions embedded in complex geometries.
Highlights
IntroductionSelf-Organised Criticality and Complexity published maps and institutional affil-. The term self-organised criticality (SOC) [1,2] describes properties of out-of-equilibrium driven dynamical systems to reach a stationary state characterised by long-range correlations, resembling the once known near the equilibrium second-order phase transitions
Self-Organised Criticality and Complexity published maps and institutional affil-The term self-organised criticality (SOC) [1,2] describes properties of out-of-equilibrium driven dynamical systems to reach a stationary state characterised by long-range correlations, resembling the once known near the equilibrium second-order phase transitions.Remarkably, in such cases, the system develops a multi-scale response involving many parts and gradually reaches a metastable state with the long-range spatial and temporal correlations without an obvious tuning parameter or a phase transition.the SOC states appear as an attractor of the nonlinear dynamics in an open system repeatedly driven by external forces
By performing a detailed analysis of the simulated magnetisation noise signals, we demonstrate SOC behaviour occurring on the hysteresis loop in these complex assemblies at the interplay of geometric frustrations and external driving
Summary
Self-Organised Criticality and Complexity published maps and institutional affil-. The term self-organised criticality (SOC) [1,2] describes properties of out-of-equilibrium driven dynamical systems to reach a stationary state characterised by long-range correlations, resembling the once known near the equilibrium second-order phase transitions. Recent surveys [2,6] reveal that, while the concept of SOC has evolved in different directions (see more discussion below), it remains a source of inspiring new research and surprising discoveries connecting the ideas of collective behaviours, the emergence and complexity, see Figure 1 In this context, the sandpile automata (SPA) models serve as the paradigm of SOC, marked by the formulation of BTW sandpile automaton [3]. The abelian nature of the dynamics (independence of the order of toppling) was one of the key features leading to the observed critical states [23] Another line of research uses continuous models and connects SOC with tropical geometry in log-log scale (which can be understood as the zero-temperature limit of classical algebraic and geometrical operations; see [28] and references there). Our study allows to identify and constructively describe the promising ways to investigate self-organised critical states under the competing higherorder interactions embedded in complex geometries
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