Dynamical Coevolution Model with Power-Law Strength
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1 2005 년 년년년년 년년년 년년년년년 Dynamical Coevolution M odel with Power-Law Str ength I. Introduc tion II. Model III. Results IV. Patholog ical region V. Summary Sungmin Lee, Yup Kim Kyung Hee Univ.
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Dynamical Coevolution Model with Power-Law Strength. I. Introduction II. Model III. Results IV. Pathological region V. Summary. Sungmin Lee, Yup Kim Kyung Hee Univ. Fitness - The fitness of each species is affected by other - PowerPoint PPT Presentation
Transcript of Dynamical Coevolution Model with Power-Law Strength
12005 년 통계물리 워크샵경기대학교
Dynamical Coevolution Model with Power-Law Strength
I. Introduction
II. Model
III. Results
IV. Pathological region
V. Summary
Sungmin Lee, Yup KimKyung Hee Univ.
22005 년 통계물리 워크샵경기대학교
I. Introduction
S.J.Gould (1972)
Instead of a slow, continuous movement, evolution
tends to be characterized by long periods of virtual
standstill ("equilibrium"), "punctuated" by episodes
of very fast development of new forms
The "punctuated equilibrium" theory
The Bak-Sneppen evolution model
0.2 0.30.15
0.40.45
0.7 0.90.35
0.10.55
0.75
0.5 0.80.65
0.60.25
Fitness - The fitness of each species is affected by other species to which it is coupled in the ecosystem.
PBC
P.Bak and K.sneppenPRL 71,4083 (1993)
0.2 0.30.15
0.40.45
0.7 0.90.95
0.47
0.22
0.75
0.5 0.80.65
0.60.25
Lowest fitness
New lowest fitness
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Snapshot of the stationary state
M.Paczuski, S.Maslov, P.BakPRE 53,414 (1996)
Avalanche - subsequent sequences of mutations through fitness below a certain threshold
Distribution of avalanche
sizes in the critical state
1d 2d
1.07(1) 1.245(10)
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Summary of previous works
◆ Random Network
◆ Scale-free Network
◆ Mean Field
S.Lee and Y.KimPRE 71, 057102 (2005)
K.Christensen et al.PRL 81, 2380 (1998)
H.Flyvbjerg et al.PRL 71, 4087 (1993)
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R.Cafiero et al. PRE 60, R1111 (1999) neighbors of the active site are chosen from power-law decreasing function of the distance
d=1
Random Neighbor
Model(MF)
S.Havlin et al. PRL 89, 218701 (2002) To each site of d-dimensional lattice, assign a random connectivity taken from power-law distribution
0.2 0.3 0.11 0.4 0.15 0.47 0.29 0.21 0.8 0.51 0.28 0.5
2 3 1 4 1 8 2 2 1 3 1 5
(degree exponent)
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II. Model
Choose update size from
the lowest fitness value
- 1d lattice with N sites (PBC)- A random fitness equally distributed
between 0 and 1, is assigned to each site.
0.2 0.3 0.11 0.4 0.45 0.7 0.9 0.01 0.1 0.55 0.75 0.5
0.2 0.3 0.11 0.4 0.15 0.47 0.29 0.21 0.8 0.51 0.28 0.5
reassign new fitness values
Motivation : dynamically changing strength
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III. Results
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1D 2D
0.66702(3) 0.328855(4)
cf)
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1D 2D
1.07(1) 1.245(10)
cf)
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1 10 100 1000 1000010-6
10-5
10-4
10-3
10-2
10-1
100
P(k)~k-2.3
=2
P(k
)
k
1 10 100 100010-6
10-5
10-4
10-3
10-2
10-1
100
P(k)~k-2.55
P(k
)
k
=2.3
1 10 10010-6
10-5
10-4
10-3
10-2
10-1
100
P(k)~k-3.8
P(k
)
k
=3
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IV. Pathological region
1 10 100 1000 1000010-6
10-5
10-4
10-3
10-2
10-1
100
=1.5
P(k
)
k1 N
all sites are updated!!
ex)
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V. Summary◆ We study modified BS model with
power-law strength.
◆ We measure the critical fitness, avalanche size distribution and degree distribution.
◆ If the base-structure is two dimension lattice the avalanche exponent approach to .
◆ The property of critical fitness changes at .
(cf. BS on SFN : )◆ The degree exponent is different from the strength exponent unlike Havlin’s network model because updates are locally occurred in our model.
