Fundamental interactions in self-organized critical dynamics on higher-order networks
arXiv:2404.06175 · doi:10.1140/epjb/s10051-024-00705-4
Abstract
In functionally complex systems, higher-order connectivity is often revealed in the underlying geometry of networked units. Furthermore, such systems often show signatures of self-organized criticality, a specific type of non-equilibrium collective behaviour associated with an attractor of internal dynamics with long-range correlations and scale invariance, which ensures the robust functioning of complex systems, such as the brain. Here, we highlight the intertwining of features of higher-order geometry and self-organized critical dynamics as a plausible mechanism for the emergence of new properties on a larger scale, representing the central paradigm of the physical notion of complexity. Considering the time scale of the structural evolution with the known separation of the time scale in self-organized criticality, i.e., internal dynamics and external driving, we distinguish three classes of geometries that can shape the self-organized dynamics on them differently. We provide an overview of current trends in the study of collective dynamics phenomena, such as the synchronization of phase oscillators and discrete spin dynamics with higher-order couplings embedded in the faces of simplicial complexes. For a representative example of self-organized critical behaviour induced by higher-order structures, we present a more detailed analysis of the dynamics of field-driven spin reversal on the hysteresis loops in simplicial complexes composed of triangles. These numerical results suggest that two fundamental interactions representing the edge-embedded and triangle-embedded couplings must be taken into account in theoretical models to describe the influence of higher-order geometry on critical dynamics.
12 pages, 4 figures
References in corpus (35)
- Multifractal detrended fluctuation analysis of nonstationary time series
- Critical phenomena in complex networks
- Are biological systems poised at criticality?
- Evolutionary dynamics of higher-order interactions in social networks
- Colloquium: Criticality and dynamical scaling in living systems
- What are higher-order networks?
- Higher-order interactions in complex networks of phase oscillators promote abrupt synchronization switching
- Spectra of complex networks
- Power laws and Self-Organized Criticality in Theory and Nature
- Network Geometry
- Network geometry with flavor: from complexity to quantum geometry
- Symmetries and Cluster Synchronization in Multilayer Networks
- Multiscale unfolding of real networks by geometric renormalization
- Self-organized criticality in the hysteresis of the Sherrington - Kirkpatrick model
- Self-organized criticality and synchronization in a lattice model of integrate-and-fire oscillators
- The mechanisms of self-organised criticality in social processes of knowledge creation
- Synchronization in Network Geometries with Finite Spectral Dimension
- Growing scale-free simplices
- Emergent spatial structures in critical sandpiles
- Global topological synchronization on simplicial and cell complexes
- 25 Years of Self-Organized Criticality: Numerical Detection Methods
- Phase Transitions and Scaling in Systems Far From Equilibrium
- Does the brain behave like a (complex) network? I. Dynamics
- Detecting the ultra low dimensionality of real networks
- Data-Driven Prediction of Thresholded Time Series of Rainfall and SOC models
- Identifying symmetries and predicting cluster synchronization in complex networks
- Disorder-induced critical behavior in driven diffusive systems
- Scale-free behavioral cascades and effective leadership in schooling fish
- Hysteresis and synchronization processes of Kuramoto oscillators on high-dimensional simplicial complexes with the competing simplex-encoded couplings
- Self-Organized Criticality and Pattern Emergence through the lens of Tropical Geometry
- Self-Organised Criticality and Emergent Hyperbolic Networks -- Blueprint for Complexity in Social Dynamics
- A devil's advocate view on 'self-organized' brain criticality
- Hidden geometry and dynamics of complex networks: Spin reversal in nanoassemblies with pairwise and triangle-based interactions
- Renormalization group analysis of a self-organized critical system: Intrinsic anisotropy vs random environment
- Effect of hidden geometry and higher-order interactions on the synchronization and hysteresis behaviour of phase oscillators on 5-cliques simplicial assemblies