Exact Results for Spatio-Temporal Correlations in a Self-Organized Critical Model of Punctuated Equilibrium

Details Exact Results for Spatio-Temporal Correlations in a Self-Organized Critical Model of Punctuated Equilibrium Exact Results for Spatio-Temporal Correlations in a Self-Organized Critical Model of Punctuated Equilibrium

1995-05-28

arxiv.org/abs/adap-org/9505003v2

Physical Review Letters 76, 348 (1996)

Physics

Condensed Matter

4 pages, postscript, uuencoded, (two ps-figures included) Final Version, to appear in PRL

Scientific paper

10.1103/PhysRevLett.76.348

We introduce a self-organized critical model of punctuated equilibrium with many internal degrees of freedom ($M$) per site. We find exact solutions for $M\rightarrow \infty$ of cascade equations describing avalanche dynamics in the steady state. This proves the existence of simple power laws with critical exponents that verify general scaling relations for nonequilibrium phenomena. Punctuated equilibrium is described by a Devil's staircase with a characteristic exponent, $\tau_{FIRST}=2-d/4$ where $d$ is the spatial dimension.

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