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
IV. Pathological region
Sungmin Lee, Yup Kim
Kyung Hee Univ.
- The fitness of each species is affected by other
species to which it is coupled in the ecosystem.
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
The Bak-Sneppen evolution model
P.Bak and K.sneppen
PRL 71,4083 (1993)
New lowest fitness
Snapshot of the stationary state
M.Paczuski, S.Maslov, P.Bak
PRE 53,414 (1996)
- subsequent sequences of mutations
through fitness below a certain threshold
Distribution of avalanche
sizes in the critical state
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
S.Havlin et al. PRL 89, 218701 (2002)
To each site of d-dimensional lattice, assign a random
connectivity taken from power-law distribution
R.Cafiero et al. PRE 60, R1111 (1999)
neighbors of the active site are chosen from power-law
decreasing function of the distance
Motivation : dynamically changing strength
- 1d lattice with N sites (PBC)
- A random fitness equally distributed between 0 and 1, is assigned to each site.
the lowest fitness value
Choose update size from
reassign new fitness values
all sites are updated!!
◆ If the base-structure is two dimension lattice the avalanche exponent approach to .
◆ 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.