How Nature Works: The Science of Self-Organized Criticality

Bak, Per; Weissman, M. B.

doi:10.1119/1.18610

Cited by 734 publications

(505 citation statements)

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“…Thus chaotic dynamics has a broadband power spectrum [59] but shows antipersistence (Hurst coefficient, H < 0.5); that is, an increasing trend in the past makes probable a decreasing trend in the future, and vice versa. In contrast to this is the persistence of 1/f noise, with H > 0.5 (H D 0.5 corresponds to uncorrelated random signal) [53,60,61]. However, at ''the edge of chaos'' -that is, the border between predictable periodic behavior and unpredictable chaos -it is possible to generate power laws [62], and 1/f noise from simple iterative maps of the logistic equation by fine-tuning the parameters of the system [53].…”

Section: Systems Biologymentioning

confidence: 97%

Chaos in Biochemistry and Physiology

Aon

Cortassa

Lloyd

2011

Encyclopedia of Molecular Cell Biology and Molecular Medicine

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Section: Systems Biologymentioning

confidence: 97%

Chaos in Biochemistry and Physiology

Aon

Cortassa

Lloyd

2011

Encyclopedia of Molecular Cell Biology and Molecular Medicine

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“…Bursts can last from a few to several hundred milliseconds and, if analyzed at a finer temporal scale, show a complex structure in terms of neuronal avalanches. As discussed in the previous chapters, neuronal avalanches exhibit dynamics similar to that of self-organized criticality (SOC), see [1][2][3][4]. Avalanches have been observed in organotypic cultures from coronal slices of rat cortex [5], where neuronal avalanches are stable for many hours [6].…”

mentioning

confidence: 88%

Activity Dependent Model for Neuronal Avalanches

Arcangelis¹,

Herrmann²

2014

Criticality in Neural Systems

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Cortical networks exhibit diverse patterns of spontaneous neural activity, including oscillations, synchrony, and waves. The spontaneous activity, often, in addition exhibits slow alternations between high activity periods, or bursts, followed by essentially quiet periods. Bursts can last from a few to several hundred milliseconds and, if analyzed at a finer temporal scale, show a complex structure in terms of neuronal avalanches. As discussed in the previous chapters, neuronal avalanches exhibit dynamics similar to that of self-organized criticality (SOC), see [1][2][3][4]. Avalanches have been observed in organotypic cultures from coronal slices of rat cortex [5], where neuronal avalanches are stable for many hours [6]. The size and duration of neuronal avalanches follow power law distributions with very stable exponents, typical features of a system in a critical state, where large fluctuations are present and system responses do not have a characteristic size. The same critical dynamics has been measured also in vivo in rat cortical layers during early postnatal development [7], in the cortex of awake adult rhesus monkeys [8], as well as in dissociated neurons from rat hippocampus [9, 10] or leech ganglia [9]. The term ''SOC'' usually refers to a mechanism of slow energy accumulation and fast energy redistribution driving the system toward a critical state, where the distribution of avalanche sizes obeys a power law obtained without fine-tuning of a particular model parameter. The simplicity of the mechanism at the basis of SOC suggests that many physical and biological phenomena characterized by power laws in the size distribution might represent natural realizations of SOC. For instance, SOC has been proposed to model earthquakes [11,12], the evolution of biological systems [13], solar flare occurrences [14], fluctuations in confined plasma [15], snow avalanches [16], and rain fall [17].While sizes and durations of avalanches have been intensively studied in neuronal systems, the quiet periods between neuronal avalanches are much less understood. In vitro preparations exhibit such quiescent periods, often called down-states which can last up to several seconds, in contrast to periods of avalanche activity, which generally are shorter in duration. The emergence of these downstates be attributed to a variety of mechanisms: a decrease in the neurotransmitter released by each synapse, either due to the exhaustion of available synaptic vesicles or to the increase of a factor inhibiting the release [18] such as the nucleoside adenosine [19]; the Criticality in Neural Systems, First Edition. Edited by Dietmar Plenz and Ernst Niebur.

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“…These clusters act as memories of past activity, shaping the path of future activity analogously to a river's flow being shaped by the past flow of water [3,65]. A recent study of model networks showed that a hierarchical topology can increase the range of parameters that give rise to critical dynamics -and thereby also the robustness of a critical state -because the modular topology limits activity spreading to local parts of the network [66].…”

Section: Multilevel Criticality: a New Class Of Dynamical Systems?mentioning

confidence: 99%