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Universal persistence exponents in an extremally driven system.

D A Head1

  • 1Department of Physics and Astronomy, JCMB King's Buildings, University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 28, 2002
PubMed
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The Bak-Sneppen model

Area of Science:

  • Complex systems
  • Statistical physics
  • Dynamical systems

Background:

  • The Bak-Sneppen model is a model of self-organized criticality.
  • Understanding the persistence of states in dynamical systems is crucial for various scientific fields.

Purpose of the Study:

  • To measure and analyze the local persistence R(t) in the Bak-Sneppen model across different dimensions.
  • To characterize the decay of R(t) based on initial configurations and system dimensionality.

Main Methods:

  • Numerical simulations of the Bak-Sneppen model in one, two, and high dimensions.
  • Analysis of the local persistence function R(t) as a function of time t.
  • Characterization of decay exponents (theta and tau(all)) and decay constants.

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Main Results:

  • In 1D and 2D, R(t) decay depends on the initial state: subcritical states show R(t) ~ t(-theta) with a universal exponent theta, while supercritical states exhibit R(t) ~ 1 - t(tau(all)) until a finite time t(0).
  • The exponent theta is related to a known universal exponent, confirming its universality.
  • In high dimensions, R(t) decays exponentially with a nonuniversal decay constant.

Conclusions:

  • The persistence behavior in the Bak-Sneppen model is dimension-dependent and sensitive to initial conditions.
  • The universality of the persistence exponent theta in lower dimensions is established.
  • High-dimensional systems exhibit distinct, nonuniversal exponential decay of persistence.