Carter, Dylan (2026) Bounds for the discrete Bak-Sneppen model. Bachelor's Thesis, Applied Mathematics.
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Abstract
We study the discrete version of the Bak-Sneppen model, where we have N species arranged in a 1-D ring formation, each with corresponding fitness values, either 0 or 1. At each step a randomly chosen zero fitness species (or one fitness in the all one’s case) as well as its 2 neighbouring species on the ring are updated with new fitness values sampled from a Bernoulli(p) random variable. We then analyse the model’s long term behaviour. The main objectives of this paper will be to present the proof from Volkov showing that for p above a certain critical threshold pc, nearly every species has fitness 1 in the stationary distribution as N → ∞ and to adapt the approach of Popov/Volkov by showing that for small p, a positive density of zeros remains, through a comparison with oriented percolation, from which we establish a numerical lower bound for the critical threshold. Finally we will run simulations to support these results as well as obtain a numerical estimate for pc.
| Item Type: | Thesis (Bachelor's Thesis) |
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| Supervisor name: | Szabo, R. and Trapman, J.P. |
| Degree programme: | Applied Mathematics |
| Thesis type: | Bachelor's Thesis |
| Language: | English |
| Date Deposited: | 03 Jul 2026 13:44 |
| Last Modified: | 03 Jul 2026 13:44 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/37333 |
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