Regulatory Dynamics on Random Networks: Asymptotic Periodicity and Modularity

TL;DR

This paper investigates the long-term behavior of discrete-time regulatory networks on random digraphs, showing almost sure convergence to periodic attractors and modular independence of oscillations.

Contribution

It introduces a framework for analyzing the asymptotic dynamics of random regulatory networks and proves the modular independence of oscillatory subnetworks.

Findings

Initial conditions almost surely lead to periodic attractors.

Modules exhibit dynamics equivalent to independent regulatory networks.

Statistical indicators characterize long-term behavior.

Abstract

We study the dynamics of discrete-time regulatory networks on random digraphs. For this we define ensembles of deterministic orbits of random regulatory networks, and introduce some statistical indicators related to the long-term dynamics of the system. We prove that, in a random regulatory network, initial conditions converge almost surely to a periodic attractor. We study the subnetworks, which we call modules, where the periodic asymptotic oscillations are concentrated. We proof that those modules are dynamically equivalent to independent regulatory networks.