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Study of Generalizations of the Discrete Bak-Sneppen Model

Panicheva, Marina LU (2021) In Bachelor's Theses in Mathematicas Sciences MASK11 20211
Mathematical 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:
author
Panicheva, Marina LU
supervisor
organization
course
MASK11 20211
year
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}},
}