Kauffman networks with threshold functions

TL;DR

This paper studies Kauffman networks with threshold functions, revealing diverse behaviors including periodic and chaotic dynamics, supported by analytical and simulation results.

Contribution

It introduces a variant of Kauffman networks with canalyzing functions and analyzes their complex behaviors beyond initial expectations.

Findings

Networks exhibit both periodic and chaotic oscillations.

Analytical calculations align with simulation results.

Behavioral richness exceeds initial criticality assumptions.

Abstract

We investigate Threshold Random Boolean Networks with $K = 2$ inputs per node, which are equivalent to Kauffman networks, with only part of the canalyzing functions as update functions. According to the simplest consideration these networks should be critical but it turns out that they show a rich variety of behaviors, including periodic and chaotic oscillations. The results are supported by analytical calculations and computer simulations.