Piccinini, Livio Clemente and Lepellere, Maria Antonietta and Chang, Ting Fa Margherita (2011): Partitioned Frames in Bak Sneppen Models.

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Abstract
In the first section we recall Bak Sneppen model and its evolutions. In this paper we wish to present some simplified cases in which explicit computations via Markov chains are possible, hence reaching a better understanding of some rather hidden phenomena of the general case: in particular “avalanches” can be read in terms of average return times and in terms of transitions between structures. A short comparison of the behaviour of different model of graphs of interaction is contained in section 2. The simple models allow us to introduce new frames that do not seem to have been considered in the previous literature, namely the case of partitioned BakSneppen frames, that appear more realistic from the point of view of speed of evolution and do not present a unique criticality level, but a staircase tending towards a final equilibrium level. This is the object of section 3, while section 4 shows how this model clearly explains the overtaking of competitors with respect to species that seem to be well assessed and recalls some of our experimental data.
Item Type:  MPRA Paper 

Original Title:  Partitioned Frames in Bak Sneppen Models 
English Title:  Partitioned frames in Bak Sneppen models 
Language:  English 
Keywords:  Punctuated equilibrium; BakSneppen models; Segmented Markov chains;globallocal interactions 
Subjects:  C  Mathematical and Quantitative Methods > C0  General C  Mathematical and Quantitative Methods > C6  Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C63  Computational Techniques ; Simulation Modeling C  Mathematical and Quantitative Methods > C0  General > C02  Mathematical Methods C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C15  Statistical Simulation Methods: General 
Item ID:  43852 
Depositing User:  Ting Fa Margherita Chang 
Date Deposited:  17 Jan 2013 15:42 
Last Modified:  27 Sep 2019 05:45 
References:  [1] P. Bak (1996) How Nature Works: The Science of SelfOrganized Criticality. Springer. [2] P. Bak, K. Sneppen (1993) Punctuated equilibrium and criticality in a simple model of evolution, Physical Review Letters,, 71(24): 40834086 [3] J. Barbay, C. Kenyon (2001) On the discrete BakSneppen model of selforganized criticality, Proc. 12th Annual ACMSIAM Symposium on discrete Algorithms, Washington DC [4] C. Bandt (2005) The discrete evolution model of Bak and Sneppen is conjugate to classical contact process J.Stat.Phys. 120, (34), 685693 [5] J. de Boer, B. Derrida, H. Flyvbjerg, A.D. Jackson, and T.Wettig, (1994) Phys. Rev. Lett. 73, 906 [6] S. Boettcher and M. Paczuski, (1996) Phys. Rev. Lett. 76, 348 [7] A. Cavalli (1998) Sociologia Enciclopedia delle Scienze Sociali, VIII, Roma [8] T. F. M. Chang – L. C. Piccinini (2000), A new Method for Analyzing UrbanRural Relations through Commutation Data, H. Hillebrand, R. Goetgeluk, H. Hetsen (eds.) Plurality and Rurality (The role of the countryside in urbanized Regions), Vol.1, LEI The Hague, pp. 102122 [ 9] P. De Los Rios, M. Marsili, M. Vendruscolo (1998) Self organized criticality in deterministic systems with disorder, Phys. Rev. Lett. 80, 5746 (1998) [10] J.S. Duesenberry (1949) Income, Savings and Theory of Consumer Behaviour Cambridge Mass..89125 [11] R.A Easterlin (1974) Does economic Growth improve the human Lot? In P.A.David and M.W.Reder eds. Nations and Households in Economic Growth Acad. Press N.Y. [12] R.A. Easterlin (2001) Income and Happiness: Towards a Unified Theory The Econ. J. 465484 [13] H. Flyvbjerg, K. Sneppen, P. Bak (1993) Mean field theory for a simple model of evolution, Phys. Rev Lett. 45, 4087 [14] C. S. Hsu (1987), Cell to cell mapping. A method of global analysis for non linear systems, Springer Vg, NY [15] M .Marsili, (1994) Europhys. Lett. 28, 385 [16] M. Marsili, P. De Los Rios, S. Maslov (1998) Expansion Around the MeanField Solution of the BakSneppen Model, Phys. Rev. Lett. 80, 1457 [17] S. Maslov (1995) Phys. Rev. Lett. 74, 562 [18] S. Maslov (1996) Infinite series of Exact Equations in the BakSneppen Model of biological evolution, Phys. Rev. Lett. 77, 1182 [19] R. Meester, C. Quant, (2005) Connections between `classical' and `selforganized' criticality, Markov processes and related _fields, 11 (2), 355370 [20] R. Meester , D. Znamenski (2002) Nontriviality of a discrete BakSneppen evolution model, J. Stat. Phys. 109, 9871004 [21] B. Mikeska (1997) Phys. Rev. E 55, 3708 [22] G. Rotundo, A. Scozzari (2008) Coevolutive Models for Firms Dynamics, Lecture notes in Economics and Mathematical systems, 613, 143158 [23] D. L. Turcotte (1999) Selforganized criticality, Rep. Prog. Phys. 62, 1377–1429 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/43852 