Predicting Criticality and Dynamic Range in Complex Networks: Effects of Topology

Daniel B. Larremore, Woodrow L. Shew, and Juan G. Restrepo
Phys. Rev. Lett. 106, 058101 – Published 31 January 2011


The collective dynamics of a network of coupled excitable systems in response to an external stimulus depends on the topology of the connections in the network. Here we develop a general theoretical approach to study the effects of network topology on dynamic range, which quantifies the range of stimulus intensities resulting in distinguishable network responses. We find that the largest eigenvalue of the weighted network adjacency matrix governs the network dynamic range. When the largest eigenvalue is exactly one, the system is in a critical state and its dynamic range is maximized. Further, we examine higher order behavior of the steady state system, which predicts that networks with more homogeneous degree distributions should have higher dynamic range. Our analysis, confirmed by numerical simulations, generalizes previous studies in terms of the largest eigenvalue of the adjacency matrix.

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  • Received 30 July 2010


© 2011 American Physical Society

Authors & Affiliations

Daniel B. Larremore1,*, Woodrow L. Shew2, and Juan G. Restrepo1

  • 1Department of Applied Mathematics, University of Colorado, Boulder, Colorado 80309, USA
  • 2National Institutes of Health, National Institute of Mental Health, Bethesda, Maryland 20892, USA

  • *

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Vol. 106, Iss. 5 — 4 February 2011

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