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Partitioned Frames in Bak Sneppen Models

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  • Piccinini, Livio Clemente
  • Lepellere, Maria Antonietta
  • Chang, Ting Fa Margherita

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 Bak-Sneppen 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.

Suggested Citation

  • Piccinini, Livio Clemente & Lepellere, Maria Antonietta & Chang, Ting Fa Margherita, 2011. "Partitioned Frames in Bak Sneppen Models," MPRA Paper 43852, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:43852
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    References listed on IDEAS

    as
    1. Easterlin, Richard A, 2001. "Income and Happiness: Towards an Unified Theory," Economic Journal, Royal Economic Society, vol. 111(473), pages 465-484, July.
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    More about this item

    Keywords

    Punctuated equilibrium; Bak-Sneppen models; Segmented Markov chains; global-local interactions;
    All these keywords.

    JEL classification:

    • C0 - Mathematical and Quantitative Methods - - General
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General

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