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Bak-Sneppen-type models and rank-driven processes

Grinfeld, Michael; Knight, Philip A.; Wade, Andrew R.

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Authors

Michael Grinfeld

Philip A. Knight



Abstract

The Bak-Sneppen model is a well-known stochastic model of evolution that exhibits self-organized criticality; only a few analytical results have been established for it so far. We report a surprising connection between Bak-Sneppen-type models and more tractable Markov processes that evolve without any reference to an underlying topology. Specifically, we show that in the case of a large number of species, the long time behavior of the fitness profile in the Bak-Sneppen model can be replicated by a model with a purely rank-based update rule whose asymptotics can be studied rigorously.

Citation

Grinfeld, M., Knight, P. A., & Wade, A. R. (2011). Bak-Sneppen-type models and rank-driven processes. Physical review E: Statistical, nonlinear, and soft matter physics, 84(4), Article 041124. https://doi.org/10.1103/physreve.84.041124

Journal Article Type Article
Publication Date Oct 1, 2011
Deposit Date Oct 4, 2012
Publicly Available Date Mar 28, 2024
Journal Physical review . E, Statistical, nonlinear, and soft matter physics
Print ISSN 1539-3755
Electronic ISSN 1550-2376
Publisher American Physical Society
Peer Reviewed Peer Reviewed
Volume 84
Issue 4
Article Number 041124
DOI https://doi.org/10.1103/physreve.84.041124

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Accepted Journal Article (492 Kb)
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Copyright Statement
© 2011 American Physical Society




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