2023/06/02 by Fink, T. M. A., Sheldon, F. C.
#Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Biological sciences #FOS: Physical sciences #Molecular Networks (q-bio.MN)
paper · doi:10.48550/arxiv.2306.01629
The Kauffman model is the archetypal model of genetic computation. It highlights the importance of criticality, at which many biological systems seem poised. In a series of advances, researchers have honed in on how the number of attractors in the critical regime grows with network size. But a definitive answer has proved elusive. We prove that, for the critical Kauffman model with connectivity one, the number of attractors grows at least, and at most, as (2/ √(e))N. This is the first proof that the number of attractors in a critical Kauffman model grows exponentially.