Dynamical coevolution model with power law strength
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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

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Dynamical Coevolution Model with Power-Law Strength

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Dynamical coevolution model with power law strength

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.


I introduction

Fitness

- The fitness of each species is affected by other

species to which it is coupled in the ecosystem.

I. Introduction

The "punctuated equilibrium" theory

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

S.J.Gould (1972)

The Bak-Sneppen evolution model

P.Bak and K.sneppen

PRL 71,4083 (1993)

Lowest fitness

PBC

New lowest fitness


Dynamical coevolution model with power law strength

Snapshot of the stationary state

M.Paczuski, S.Maslov, P.Bak

PRE 53,414 (1996)

Avalanche

- subsequent sequences of mutations

through fitness below a certain threshold

Distribution of avalanche

sizes in the critical state


Dynamical coevolution model with power law strength

Summary of previous works

H.Flyvbjerg et al.

PRL 71, 4087 (1993)

◆ Mean Field

◆ Random Network

K.Christensen et al.

PRL 81, 2380 (1998)

S.Lee and Y.Kim

PRE 71, 057102 (2005)

◆ Scale-free Network


Dynamical coevolution model with power law strength

0.2

0.3

0.11

0.4

0.15

0.47

0.29

0.21

0.8

0.51

0.28

0.5

Random

Neighbor

Model

(MF)

d=1

S.Havlin et al. PRL 89, 218701 (2002)

To each site of d-dimensional lattice, assign a random

connectivity taken from power-law distribution

2

3

1

4

1

8

2

2

1

3

1

5

R.Cafiero et al. PRE 60, R1111 (1999)

neighbors of the active site are chosen from power-law

decreasing function of the distance

(degree exponent)


Ii model

Motivation : dynamically changing strength

0.2

0.3

0.11

0.4

0.15

0.47

0.29

0.21

0.8

0.51

0.28

0.5

II. Model

- 1d lattice with N sites (PBC)

- A random fitness equally distributed between 0 and 1, is assigned to each site.

the lowest fitness value

0.2

0.3

0.11

0.4

0.45

0.7

0.9

0.01

0.1

0.55

0.75

0.5

Choose update size from

reassign new fitness values


Iii results

III. Results


Dynamical coevolution model with power law strength

cf)


Dynamical coevolution model with power law strength

cf)


Iv pathological region

N

1

all sites are updated!!

IV. Pathological region

ex)


V summary

◆ If the base-structure is two dimension lattice the avalanche exponent approach to .

V. Summary

◆ We study modified BS model with power-law strength.

◆ We measure the critical fitness, avalanche size distribution and degree distribution.

◆ 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.


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