Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Accuracy of a one-dimensional reduction of dynamical systems on networks   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 et al. proposed a theoretical framework
to reduce dynamical systems on networks, which are high dimensional in general,
to one-dimensional dynamical systems. The accuracy of this one-dimensional
reduction relies on several assumption in addition to the assumption that the
network has a negligible degree correlation. In the present study, we analyze
the accuracy of the one-dimensional 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 one-dimensional reduction hinges on the spread of the
equilibrium value of the state variable across the nodes in most cases.
Specifically, the one-dimensional 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
one-dimensional reduction.

23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
20
The categories of this paper are: acc-phys
1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
19
The categories of this paper are: eess
34
The categories of this paper are: chem-ph
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph