Attractors in continuous and Boolean networks

Johannes Norrell, Björn Samuelsson, and Joshua E. S. Socolar
Phys. Rev. E 76, 046122 – Published 30 October 2007

Abstract

We study the stable attractors of a class of continuous dynamical systems that may be idealized as networks of Boolean elements, with the goal of determining which Boolean attractors, if any, are good approximations of the attractors of generic continuous systems. We investigate the dynamics in simple rings and rings with one additional self-input. An analysis of switching characteristics and pulse propagation explains the relation between attractors of the continuous systems and their Boolean approximations. For simple rings, “reliable” Boolean attractors correspond to stable continuous attractors. For networks with more complex logic, the qualitative features of continuous attractors are influenced by inherently non-Boolean characteristics of switching events.

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  • Received 30 January 2007

DOI:https://doi.org/10.1103/PhysRevE.76.046122

©2007 American Physical Society

Authors & Affiliations

Johannes Norrell, Björn Samuelsson, and Joshua E. S. Socolar

  • Physics Department and Center for Nonlinear and Complex Systems, Duke University, Durham, North Carolina 27708, USA

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Issue

Vol. 76, Iss. 4 — October 2007

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