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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. 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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  1. 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.

  2. 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

  3. 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

  4. 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

  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 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)

  6. 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

  7. III. Results

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  10. N 1 all sites are updated!! IV. Pathological region ex)

  11. ◆ 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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