Kauffman networks with threshold functions

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.

4 pages, submitted to PhysRev; http://www.edpsciences.org/10.1140/epjb/e2007-00161-0

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Cited by in corpus (11)

• Boolean Delay Equations: A simple way of looking at complex systems
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• The phase diagram of random Boolean networks with nested canalizing functions
• Stability of Boolean networks: The joint effects of topology and update rules
• Critical Line in Random Threshold Networks with Inhomogeneous Thresholds
• Influence and Dynamic Behavior in Random Boolean Networks
• Large attractors in cooperative bi-quadratic Boolean networks. Part II
• Circuits, Attractors and Reachability in Mixed-K Kauffman Networks
• Mean-Field and Non-Mean-Field Behaviors in Scale-free Networks with Random Boolean Dynamics
• Stability in random Boolean cellular automata on the integer lattice
• An Extensive Study of Two-Node McCulloch-Pitts Networks