2018/03/05 by Christophe Letellier, I. Sendiña–Nadal, Irene Sendiña-Nadal +2 · 1 citation
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · Neuroscience · Physics and Astronomy · #Applied mathematics #Combinatorics #Computer science #Dynamical systems theory #Gene Regulatory Network Analysis #Graph #Jacobian matrix and determinant #Mathematical optimization #Mathematics #Neural dynamics and brain function #Node (physics) #Nonlinear Dynamics and Pattern Formation #Nonlinear system #Observability #Observable #State space #State variable #Theoretical computer science #Topology (electrical circuits) #nlin.CD
paper · pdf · doi:10.1103/physreve.98.020303
published as Phys. Rev. E 98, 020303 (2018) · 5 pages, 2 figures; added references
arxiv created 2018/03/05 · openalex publication_date 2018/08/28 · arxiv updated 2019/05/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A faithful description of the state of a complex dynamical network would require, in principle, the measurement of all its d variables, an infeasible task for high dimensional systems due to practical limitations. However the network dynamics might be observable from a reduced set of measured variables but how to reliably identify the minimum set of variables providing full observability still remains an unsolved problem. In order to tackle this issue from the Jacobian matrix of the governing equations, we construct a pruned fluence graph in which the nodes are the state variables and the links represent only the linear dynamical interdependences after having ignored the nonlinear ones. From this graph, we identify the largest connected subgraphs with no outgoing links in which every node can be reached from any other node in the subgraph. In each one of them, at least one node must be measured to correctly monitor the state of the system in a d-dimensional reconstructed space. Our procedure is here tested by investigating large-dimensional reaction networks. Our results are validated by comparing them with the determinant of the observability matrix which provides a rigorous assessment of the system's observability.