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arXiv · 2302.05314

Exact dynamics of the critical Kauffman model with connectivity one

T. M. A. Fink
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Abstract

The critical Kauffman model with connectivity one is the simplest class of critical Boolean networks. Nevertheless, it exhibits intricate behavior at the boundary of order and chaos. We introduce a formalism for expressing the dynamics of multiple loops as a product of the dynamics of individual loops. Using it, we prove that the number of attractors scales as $2^m$, where $m$ is the number of nodes in loops - as fast as possible, and much faster than previously believed.

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T. M. A. Fink. 2023-02-10. Exact dynamics of the critical Kauffman model with connectivity one. https://arxiv.org/abs/2302.05314

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