Brief paper: Design of highly synchronizable and robust networks

  • Authors:

  • Ernesto Estrada;Silvia Gago;Gilles Caporossi

  • Affiliations:

  • Department of Mathematics and Statistics, University of Strathclyde, Glasgow, G1 1XQ, UK and Department of Physics and Institute of Complex Systems, University of Strathclyde, Glasgow, G1 1XQ, UK;Department de Matemítica Aplicada IV, EPSC, Universitat Politècnica de Catalunya, Av. Canal Olímpic s/n, 08860 Castelldefels, Spain;Department of Management Sciences, HEC Montréal 3000, chemin de la Côte-Sainte-Catherine, Montréal (Québec), Canada H3T 2A7

  • Venue:
  • Automatica (Journal of IFAC)
  • Year:
  • 2010

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Abstract

In this paper, the design of highly synchronizable, sparse and robust dynamical networks is addressed. Better synchronizability means faster synchronization of the oscillators, sparsity means a low ratio of links per nodes and robustness refers to the resilience of a network to the random failures or intentional removal of some of the nodes/links. Golden spectral dynamical networks (graphs) are those for which the spectral spread (the difference between the largest and smallest eigenvalues of the adjacency matrix) is equal to the spectral gap (the difference between the two largest eigenvalues of the adjacency matrix) multiplied by the square of the golden ratio. These networks display the property of ''small-worldness'', are very homogeneous and have large isoperimetric (expansion) constant, together with a very high synchronizability and robustness to failures of individual oscillators. In particular, the regular bipartite dynamical networks, reported here by the first time, have the best possible expansion and consequently are the most robust ones against node/link failures or intentional attacks.