Generalizations of the Discrete BakSneppen Model
(2020) In Bachelor's Theses in Mathematical Sciences MASK11 20201Mathematical Statistics
 Abstract
 Consider n vertices arranged in a circle where each vertex is given a fitness from {0,1}. At each discrete time step, one of the vertices with fitness equal to zero (unless there are none of those, then pick a vertex with fitness equal to one) is selected with equal probability. Then this vertex and the two neighbouring vertices are each given a new fitness from a Bernoulli(p) distribution independently of each other, for some p in [0,1]. This model is known as the discrete BakSneppen model. What happens to the fraction of ones (vertices with fitness one) as n and the time t goes to infinity? How does this quantity depend on p? Is there a pc in (0,1) such that this quantity is equal to one for p > pc and less than one for p < pc? In this... (More)
 Consider n vertices arranged in a circle where each vertex is given a fitness from {0,1}. At each discrete time step, one of the vertices with fitness equal to zero (unless there are none of those, then pick a vertex with fitness equal to one) is selected with equal probability. Then this vertex and the two neighbouring vertices are each given a new fitness from a Bernoulli(p) distribution independently of each other, for some p in [0,1]. This model is known as the discrete BakSneppen model. What happens to the fraction of ones (vertices with fitness one) as n and the time t goes to infinity? How does this quantity depend on p? Is there a pc in (0,1) such that this quantity is equal to one for p > pc and less than one for p < pc? In this paper we prove upper bounds for pc for generalized versions of this model. We alsoprovide a number of experimental results, as well as a quick summary of what hasbeen done in the past. (Less)
 Popular Abstract
 The BakSneppen model is a simple model of coevolution. It can be viewed as a simplified version of how different species interact with each other in nature. It takes into account the randomness of evolution as well as the idea of the survival of the fittest. Even though this model is very simple compared to the real world, it is not yet fully understood. Maybe in order to understand it better we should first try to understand an even simpler model, namely the discrete BakSneppen model. The main topic of this paper will be to generalize the discrete BakSneppen modeland to prove relevant properties to it. We will also provide experimental results of these properties as well as for the properties that are left unproven.
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/studentpapers/record/9012003
 author
 Jönsson, John ^{LU}
 supervisor

 Stanislav Volkov ^{LU}
 organization
 course
 MASK11 20201
 year
 2020
 type
 M2  Bachelor Degree
 subject
 keywords
 discrete, BakSneppen, model, generalized, probability, Markov
 publication/series
 Bachelor's Theses in Mathematical Sciences
 report number
 LUNFMS40452020
 ISSN
 16546229
 other publication id
 2020:K10
 language
 English
 id
 9012003
 date added to LUP
 20200612 11:43:13
 date last changed
 20200615 15:37:58
@misc{9012003, abstract = {Consider n vertices arranged in a circle where each vertex is given a fitness from {0,1}. At each discrete time step, one of the vertices with fitness equal to zero (unless there are none of those, then pick a vertex with fitness equal to one) is selected with equal probability. Then this vertex and the two neighbouring vertices are each given a new fitness from a Bernoulli(p) distribution independently of each other, for some p in [0,1]. This model is known as the discrete BakSneppen model. What happens to the fraction of ones (vertices with fitness one) as n and the time t goes to infinity? How does this quantity depend on p? Is there a pc in (0,1) such that this quantity is equal to one for p > pc and less than one for p < pc? In this paper we prove upper bounds for pc for generalized versions of this model. We alsoprovide a number of experimental results, as well as a quick summary of what hasbeen done in the past.}, author = {Jönsson, John}, issn = {16546229}, keyword = {discrete,BakSneppen,model,generalized,probability,Markov}, language = {eng}, note = {Student Paper}, series = {Bachelor's Theses in Mathematical Sciences}, title = {Generalizations of the Discrete BakSneppen Model}, year = {2020}, }