Dynamical Properties of Random Boolean Hypernetworks

TL;DR

This paper introduces Boolean hypernetworks, extending standard Boolean networks to include multi-way interactions, and analyzes how these additions influence the stability and dynamics of the systems.

Contribution

The paper proposes Boolean hypernetworks as a generalization of Boolean networks and explores their properties through derived ensembles and simulations.

Findings

Multi-way interactions affect network stability.

Addition of hyperedges can stabilize or destabilize dynamics.

Boolean hypernetworks generalize standard models.

Abstract

Boolean networks are a valuable class of discrete dynamical systems models, but they remain fundamentally limited by their inability to capture multi-way interactions in their components. To remedy this limitation, we propose a model of Boolean hypernetworks, which generalize standard Boolean networks. Utilizing the bijection between hypernetworks and bipartite networks, we show how Boolean hypernetworks generalize standard Boolean networks. We derive ensembles of Boolean hypernetworks from standard random Boolean networks and simulate the dynamics of each. Our results indicate that several properties of Boolean network dynamics are affected by the addition of multi-way interactions, and that these additions can have stabilizing or destabilizing effects.