9,788 research outputs found
Effect of correlations on network controllability
A dynamical system is controllable if by imposing appropriate external
signals on a subset of its nodes, it can be driven from any initial state to
any desired state in finite time. Here we study the impact of various network
characteristics on the minimal number of driver nodes required to control a
network. We find that clustering and modularity have no discernible impact, but
the symmetries of the underlying matching problem can produce linear, quadratic
or no dependence on degree correlation coefficients, depending on the nature of
the underlying correlations. The results are supported by numerical simulations
and help narrow the observed gap between the predicted and the observed number
of driver nodes in real networks
Control of Multilayer Networks
The controllability of a network is a theoretical problem of relevance in a
variety of contexts ranging from financial markets to the brain. Until now,
network controllability has been characterized only on isolated networks, while
the vast majority of complex systems are formed by multilayer networks. Here we
build a theoretical framework for the linear controllability of multilayer
networks by mapping the problem into a combinatorial matching problem. We found
that correlating the external signals in the different layers can significantly
reduce the multiplex network robustness to node removal, as it can be seen in
conjunction with a hybrid phase transition occurring in interacting Poisson
networks. Moreover we observe that multilayer networks can stabilize the fully
controllable multiplex network configuration that can be stable also when the
full controllability of the single network is not stable
Controlling edge dynamics in complex networks
The interaction of distinct units in physical, social, biological and
technological systems naturally gives rise to complex network structures.
Networks have constantly been in the focus of research for the last decade,
with considerable advances in the description of their structural and dynamical
properties. However, much less effort has been devoted to studying the
controllability of the dynamics taking place on them. Here we introduce and
evaluate a dynamical process defined on the edges of a network, and demonstrate
that the controllability properties of this process significantly differ from
simple nodal dynamics. Evaluation of real-world networks indicates that most of
them are more controllable than their randomized counterparts. We also find
that transcriptional regulatory networks are particularly easy to control.
Analytic calculations show that networks with scale-free degree distributions
have better controllability properties than uncorrelated networks, and
positively correlated in- and out-degrees enhance the controllability of the
proposed dynamics.Comment: Preprint. 24 pages, 4 figures, 2 tables. Source code available at
http://github.com/ntamas/netctr
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