Accuracy of a onedimensional reduction of dynamical systems on networks
Abstract
Resilience is an ability of a system with which the system can adjust its activity to maintain its functionality when it is perturbed. To study resilience of dynamics on networks, Gao {\it et al.} [Nature, {\bf{530}}, 307 (2016)] proposed a theoretical framework to reduce dynamical systems on networks, which are highdimensional in general, to onedimensional dynamical systems. The accuracy of this onedimensional reduction relies on several assumptions in addition to that the network has a negligible degree correlation. In the present study, we analyze the accuracy of the onedimensional reduction assuming networks without degree correlation. We do so mainly through examining the validity of the individual assumptions underlying the method. Across five dynamical system models, we find that the accuracy of the onedimensional reduction hinges on the spread of the equilibrium value of the state variable across the nodes in most cases. Specifically, the onedimensional reduction tends to be accurate when the dispersion of the node's state is small. We also find that the correlation between the node's state and the node's degree, which is common for various dynamical systems on networks, is unrelated to the accuracy of the onedimensional reduction.
 Publication:

arXiv eprints
 Pub Date:
 October 2021
 arXiv:
 arXiv:2110.07140
 Bibcode:
 2021arXiv211007140K
 Keywords:

 Physics  Physics and Society;
 Nonlinear Sciences  Adaptation and SelfOrganizing Systems
 EPrint:
 35 pages, 15 figures