Percolation and depinning transitions in cut-and-paste models of adaptation

Details Percolation and depinning transitions in cut-and-paste models of adaptation Percolation and depinning transitions in cut-and-paste models of adaptation

2001-05-29

arxiv.org/abs/cond-mat/0105556v2

Physics

Condensed Matter

Statistical Mechanics

9 pages, 6 figures, submitted to publication should work with Ghostview, thanks Sid

Scientific paper

10.1016/S0378-4371(02)00555-1

We show that a cut-and-paste model to mimic a trial-and-error process of adaptation displays two pairs of percolation and depinning transitions, one for persistence and the other for efficiency. The percolation transition signals the onset of a property and the depinning transition, the growth of the same property. Despite its simplicity, the cut-and-paste model is qualitatively the same as the Minority Game. A majority cut-and-paste model is also introduced, to mimic the spread of a trend. When both models are iterated, the majority model reaches a frozen state while the minority model converges towards an alternate state. We show that a transition from the frozen to the alternate state occurs in the limit of a non-adaptive system.

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