Power laws and Self-Organized Criticality in Theory and Nature

By Dimitrije Marković, Claudius Gros. 2013

280 citations recorded by the source corpus.

Abstract Power laws and distributions with heavy tails are common features of many complex systems. Examples are the distribution of earthquake magnitudes, solar flare intensities and the sizes of neuronal avalanches. Previously, researchers surmised that a single general concept may act as an underlying generative mechanism, with the theory of self organized criticality being a weighty contender. The power-law scaling observed in the primary statistical analysis is an important, but by far not the only feature characterizing experimental data. The scaling function, the distribution of energy fluctuations, the distribution of inter-event waiting times, and other higher order spatial and temporal correlations, have seen increased consideration over the last years. Leading to realization that basic models, like the original sandpile model, are often insufficient to adequately describe the complexity of real-world systems with power-law distribution. Consequently, a substantial amount of effort has gone into developing new and extended models and, hitherto, three classes of models have emerged. The first line of models is based on a separation between the time scales of an external drive and an internal dissipation, and includes the original sandpile model and its extensions, like the dissipative earthquake model. Within this approach the steady state is close to criticality in terms of an absorbing phase transition. The second line of models is based on external drives and internal dynamics competing on similar time scales and includes the coherent noise model, which has a non-critical steady state characterized by heavy-tailed distributions. The third line of models proposes a non-critical self-organizing state, being guided by an optimization principle, such as the concept of highly optimized tolerance. We present a comparative overview regarding distinct modeling approaches together with a discussion of their potential relevance as underlying generative models for real-world phenomena. The complexity of physical and biological scaling phenomena has been found to transcend the explanatory power of individual paradigmal concepts. The interaction between theoretical development and experimental observations has been very fruitful, leading to a series of novel concepts and insights.

Subfields: Condensed Matter Physics, Geophysics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/47533821afff99704cfba489a95c4e01eb4d7bf6

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In Condensed Matter Physics

Miguel Angel Muñoz

In Geophysics

Miguel Angel Muñoz

In Statistical and Nonlinear Physics

Citations in the corpus

Criticality in the brain: A synthesis of neurobiology, models and cognition. (2017, background): “ween the fast system dynamics and the slow build up and dissipation of energy. Criticality in the brain Cocchi et al. 19 19 Several models of criticality in the brain incorporate such slow processes (Marković and Gros, 2014). A considerable body of research has focused upon the role of various forms”
Colloquium: Criticality and dynamical scaling in living systems (2017, background): “5 From the mathematical side, very diverse explanatory mechanisms for the emergence of scaling in empirical data have been put forward (Marković and Gros, 2014; Mitzenmacher, 2002; Newman, 2005; Simkin and Roychowdhury, 2011; Sornette, 2009).”
Self-organized criticality as a fundamental property of neural systems (2014, background): “For example, the shapes of avalanches of any size resemble each other (Marković and Gros, 2014).”
Glutamatergic and GABAergic Receptor Modulation Present Unique Electrophysiological Fingerprints in a Concentration-Dependent and Region-Specific Manner (2023, background): “The EEG shows a power spectrum (PS) following a 1/f pattern that reveals an intrinsic feature of many complex systems in nature (Freeman et al., 2003; Miller et al., 2009; Markovi c and Gros, 2014).”