Study of Generalizations of the Discrete Bak-Sneppen Model
(2021) In Bachelor's Theses in Mathematicas Sciences MASK11 20211Mathematical Statistics
- Abstract (Swedish)
- In 1993, Per Bak and Kim Sneppen proposed a model of co-evolution between
species, where survival of a particular species affects the survival of its
neighbouring species. In the discrete case of the model, each species, or an
entry in a set with periodic boundary conditions, is an element x_i ∈ {0, 1},
in the set of size N, where x_i represents the fitness. An entry of the least
fitness is chosen and replaced together with its two neighbours each with
Bernoulli(p), p ∈ [0, 1] random variables. If the parameter p is larger than
some p_cr, the whole set is eventually consumed by 1.
In this paper, we study the generalizations of the discrete case of Bak-
Sneppen model and evaluate p_cr both analytically and numerically. For that
... (More) - In 1993, Per Bak and Kim Sneppen proposed a model of co-evolution between
species, where survival of a particular species affects the survival of its
neighbouring species. In the discrete case of the model, each species, or an
entry in a set with periodic boundary conditions, is an element x_i ∈ {0, 1},
in the set of size N, where x_i represents the fitness. An entry of the least
fitness is chosen and replaced together with its two neighbours each with
Bernoulli(p), p ∈ [0, 1] random variables. If the parameter p is larger than
some p_cr, the whole set is eventually consumed by 1.
In this paper, we study the generalizations of the discrete case of Bak-
Sneppen model and evaluate p_cr both analytically and numerically. For that
end, we first examine the case where in each iteration a vertex x_i and its
both neighbours x_{i−1}, x_{i+1} are replaced by the same Bernoulli(p) variable.
Then, we study the case where the type of the model - whether the entry
is replaced alone or with its neighbours - is determined by a Bernoulli(r)
variable. Finally, we find a non-trivial p_cr for a 2-dimentional set of entries. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/student-papers/record/9068539
- author
- Panicheva, Marina LU
- supervisor
- organization
- course
- MASK11 20211
- year
- 2021
- type
- M2 - Bachelor Degree
- subject
- keywords
- Bak-Sneppen, Discrete Bak-Sneppen, co-evolution, self-organized criticality
- publication/series
- Bachelor's Theses in Mathematicas Sciences
- report number
- LUNFMS-4060-2021
- ISSN
- 1654-6229
- other publication id
- 2021:K36
- language
- English
- id
- 9068539
- date added to LUP
- 2022-02-02 10:52:42
- date last changed
- 2022-02-02 14:11:07
@misc{9068539, abstract = {{In 1993, Per Bak and Kim Sneppen proposed a model of co-evolution between species, where survival of a particular species affects the survival of its neighbouring species. In the discrete case of the model, each species, or an entry in a set with periodic boundary conditions, is an element x_i ∈ {0, 1}, in the set of size N, where x_i represents the fitness. An entry of the least fitness is chosen and replaced together with its two neighbours each with Bernoulli(p), p ∈ [0, 1] random variables. If the parameter p is larger than some p_cr, the whole set is eventually consumed by 1. In this paper, we study the generalizations of the discrete case of Bak- Sneppen model and evaluate p_cr both analytically and numerically. For that end, we first examine the case where in each iteration a vertex x_i and its both neighbours x_{i−1}, x_{i+1} are replaced by the same Bernoulli(p) variable. Then, we study the case where the type of the model - whether the entry is replaced alone or with its neighbours - is determined by a Bernoulli(r) variable. Finally, we find a non-trivial p_cr for a 2-dimentional set of entries.}}, author = {{Panicheva, Marina}}, issn = {{1654-6229}}, language = {{eng}}, note = {{Student Paper}}, series = {{Bachelor's Theses in Mathematicas Sciences}}, title = {{Study of Generalizations of the Discrete Bak-Sneppen Model}}, year = {{2021}}, }