Controlling Statistical Moments of Stochastic Dynamical Networks

TL;DR

This paper develops a method to control the statistical moments of stochastic networks by identifying key nodes for intervention, enabling stabilization and switching between target states while preserving covariance structure.

Contribution

It introduces a graph-based approach to determine which nodes to control and a feedback method to maintain desired statistical properties in stochastic networks.

Findings

Control of moments achieved in stochastic Hopfield network

Method preserves covariance structure of target states

Applicable to various network models

Abstract

We consider a general class of stochastic networks and ask which network nodes need to be controlled, and how, to stabilize and switch between desired metastable (target) states in terms of the first and second statistical moments of the system. We first show that it is sufficient to directly interfere with a subset of nodes which can be identified using information about the graph of the network only. Then, we develop a suitable method for feedback control which acts on that subset of nodes and preserves the covariance structure of the desired target state. Finally, we demonstrate our theoretical results using a stochastic Hopfield network and a global brain model. Our results are applicable to a variety of (model) networks, and further our understanding of the relationship between network structure and collective dynamics for the benefit of effective control.