Controllability of Complex Networks

Overview

Journal Nature

Specialty Science

Date 2011 May 13

PMID 21562557

Citations 536

Authors

Yang-Yu Liu

Jean-Jacques Slotine

Albert-Laszlo Barabasi

Affiliations

Soon will be listed here.

Abstract

The ultimate proof of our understanding of natural or technological systems is reflected in our ability to control them. Although control theory offers mathematical tools for steering engineered and natural systems towards a desired state, a framework to control complex self-organized systems is lacking. Here we develop analytical tools to study the controllability of an arbitrary complex directed network, identifying the set of driver nodes with time-dependent control that can guide the system's entire dynamics. We apply these tools to several real networks, finding that the number of driver nodes is determined mainly by the network's degree distribution. We show that sparse inhomogeneous networks, which emerge in many real complex systems, are the most difficult to control, but that dense and homogeneous networks can be controlled using a few driver nodes. Counterintuitively, we find that in both model and real systems the driver nodes tend to avoid the high-degree nodes.

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References

Lezon T, Banavar J, Cieplak M, Maritan A, Fedoroff N . Using the principle of entropy maximization to infer genetic interaction networks from gene expression patterns. Proc Natl Acad Sci U S A. 2006; 103(50):19033-8. PMC: 1748172. DOI: 10.1073/pnas.0609152103. View

Motter A, Gulbahce N, Almaas E, Barabasi A . Predicting synthetic rescues in metabolic networks. Mol Syst Biol. 2008; 4:168. PMC: 2267730. DOI: 10.1038/msb.2008.1. View

Maslov S, Sneppen K . Specificity and stability in topology of protein networks. Science. 2002; 296(5569):910-3. DOI: 10.1126/science.1065103. View

Goh K, Kahng B, Kim D . Universal behavior of load distribution in scale-free networks. Phys Rev Lett. 2002; 87(27 Pt 1):278701. DOI: 10.1103/PhysRevLett.87.278701. View

Marucci L, Barton D, Cantone I, Ricci M, Cosma M, Santini S . How to turn a genetic circuit into a synthetic tunable oscillator, or a bistable switch. PLoS One. 2009; 4(12):e8083. PMC: 2784219. DOI: 10.1371/journal.pone.0008083. View

Barabasi , ALBERT . Emergence of scaling in random networks. Science. 1999; 286(5439):509-12. DOI: 10.1126/science.286.5439.509. View

Wang W, Slotine J . On partial contraction analysis for coupled nonlinear oscillators. Biol Cybern. 2005; 92(1):38-53. DOI: 10.1007/s00422-004-0527-x. View

Pastor-Satorras R, Vespignani A . Epidemic spreading in scale-free networks. Phys Rev Lett. 2001; 86(14):3200-3. DOI: 10.1103/PhysRevLett.86.3200. View

Callaway D, Newman M, Strogatz S, Watts D . Network robustness and fragility: percolation on random graphs. Phys Rev Lett. 2001; 85(25):5468-71. DOI: 10.1103/PhysRevLett.85.5468. View

10.

Cohen , Erez , Havlin . Resilience of the internet to random breakdowns. Phys Rev Lett. 2000; 85(21):4626-8. DOI: 10.1103/PhysRevLett.85.4626. View

11.

Pastor-Satorras R, Vazquez A, Vespignani A . Dynamical and correlation properties of the internet. Phys Rev Lett. 2001; 87(25):258701. DOI: 10.1103/PhysRevLett.87.258701. View

12.

Nishikawa T, Motter A, Lai Y, Hoppensteadt F . Heterogeneity in oscillator networks: are smaller worlds easier to synchronize?. Phys Rev Lett. 2003; 91(1):014101. DOI: 10.1103/PhysRevLett.91.014101. View

13.

Yu W, Chen G, Cao M, Kurths J . Second-order consensus for multiagent systems with directed topologies and nonlinear dynamics. IEEE Trans Syst Man Cybern B Cybern. 2009; 40(3):881-91. DOI: 10.1109/TSMCB.2009.2031624. View

14.

ALBERT , Jeong , Barabasi . Error and attack tolerance of complex networks. Nature. 2000; 406(6794):378-82. DOI: 10.1038/35019019. View

15.

Lombardi A, Hornquist M . Controllability analysis of networks. Phys Rev E Stat Nonlin Soft Matter Phys. 2007; 75(5 Pt 2):056110. DOI: 10.1103/PhysRevE.75.056110. View

16.

Newman M . Assortative mixing in networks. Phys Rev Lett. 2002; 89(20):208701. DOI: 10.1103/PhysRevLett.89.208701. View

17.

Sorrentino F, di Bernardo M, Garofalo F, Chen G . Controllability of complex networks via pinning. Phys Rev E Stat Nonlin Soft Matter Phys. 2007; 75(4 Pt 2):046103. DOI: 10.1103/PhysRevE.75.046103. View

18.

Strogatz S . Exploring complex networks. Nature. 2001; 410(6825):268-76. DOI: 10.1038/35065725. View

19.

Milo R, Itzkovitz S, Kashtan N, Chklovskii D, Alon U . Network motifs: simple building blocks of complex networks. Science. 2002; 298(5594):824-7. DOI: 10.1126/science.298.5594.824. View