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Self-Organized Branching Processes: Mean-Field Theory for Avalanches
Open accessAbstract
We discuss mean-field theories for self-organized criticality and the connection with the general theory of branching processes. We point out that the nature of the self-organization is not addressed properly by the previously proposed mean-field theories. We introduce a new mean-field model that explicitly takes the boundary conditions into account; in this way, the local dynamical rules are coupled to a global equation that drives the control parameter to its critical value. We study the model numerically, and analytically we compute the avalanche distributions.
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Cited by
Neuronal Avalanches in Neocortical Circuits
Beggs, J. M., & Plenz, D. (2003) · The Journal of Neuroscience · doi:10.1523/jneurosci.23-35-11167.2003 · Cited by 2,325
Emergent complex neural dynamics
Chialvo, D. R. (2010) · Nature Physics · doi:10.1038/nphys1803 · Cited by 1,165
Are Biological Systems Poised at Criticality?
Mora, T., & Bialek, W. (2011) · Journal of Statistical Physics · doi:10.1007/s10955-011-0229-4 · Cited by 734
Vogels, T. P., Rajan, K., & Abbott, L. F. (2005) · Annual Review of Neuroscience · doi:10.1146/annurev.neuro.28.061604.135637 · Cited by 497
Signal Propagation and Logic Gating in Networks of Integrate-and-Fire Neurons
Vogels, T. P., & Abbott, L. F. (2005) · The Journal of Neuroscience · doi:10.1523/jneurosci.3508-05.2005 · Cited by 465
Metadata
- Authors
- Zapperi, S., Lauritsen, K. B., & Stanley, H. E.
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 1995-11-27
- Volume
- 75
- Issue
- 22
- Pages
- 4071-4074
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W1992064183
- Cited by
- 304
- References
- 0
- FWCI
- 5.11
- Type
- journal article
- Language
- en
- Open access
- green
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- Zapperi, S., Lauritsen, K. B., & Stanley, H. E. (1995). Self-Organized Branching Processes: Mean-Field Theory for Avalanches. Physical Review Letters. https://doi.org/10.1103/physrevlett.75.4071
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