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Controlling Statistical Moments of Stochastic Dynamical Networks
Citation key Bielivtsov2016
Author Bielivtsov, D. and Ladenbauer, J. and Obermayer, K.
Pages 012306
Year 2016
DOI 10.1103/PhysRevE.94.012306
Journal Physical Review E
Volume 94
Number 1
Publisher American Physical Society
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 guarantees to preserve the covariance structure of the desired target state. Finally, we demonstrate our theoretical results using a stochastic Hopfield network as an example. 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.
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