Attractors in continuous and Boolean networks

Details Attractors in continuous and Boolean networks Attractors in continuous and Boolean networks

2007-01-30

arxiv.org/abs/q-bio/0701052v3

Biology

Quantitative Biology

Molecular Networks

Revised and extended version. The methods section from version 2 is now an appendix and another appendix has been added. Submi

Scientific paper

10.1103/PhysRevE.76.046122

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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