Bak-Sneppen-type models and rank-driven processes

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

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: Jan 31, 2013
• 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
• Public URL: https://durham-repository.worktribe.com/output/1502796