No Access Submitted: 02 February 2016 Accepted: 28 March 2016 Published Online: 02 June 2016
Chaos 26, 065302 (2016); https://doi.org/10.1063/1.4952960
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  • Andrea Girón
  • Hugo Saiz
  • Flora S. Bacelar
  • Roberto F. S. Andrade
  • Jesús Gómez-Gardeñes
Network science has helped to understand the organization principles of the interactions among the constituents of large complex systems. However, recently, the high resolution of the data sets collected has allowed to capture the different types of interactions coexisting within the same system. A particularly important example is that of systems with positive and negative interactions, a usual feature appearing in social, neural, and ecological systems. The interplay of links of opposite sign presents natural difficulties for generalizing typical concepts and tools applied to unsigned networks and, moreover, poses some questions intrinsic to the signed nature of the network, such as how are negative interactions balanced by positive ones so to allow the coexistence and survival of competitors/foes within the same system? Here, we show that synchronization phenomenon is an ideal benchmark for uncovering such balance and, as a byproduct, to assess which nodes play a critical role in the overall organization of the system. We illustrate our findings with the analysis of synthetic and real ecological networks in which facilitation and competitive interactions coexist.
We are grateful to Concepción L. Alados and Yolanda Pueyo who kindly shared their data about Monegros (CGL2012-37508) and Cabo de Gata (CGL2011-27259). J.G.G. acknowledges financial support from the European Commission through FET IP projects MULTIPLEX (Grant No. 317532) and PLEXMATH (Grant No. 317614), the Spanish MINECO through the Ramón y Cajal program and Projects FIS2015-71582-C2 and FIS2014-55867-P, from the Departamento de Industria e Innovación del Gobierno de Aragón y Fondo Social Europeo (FENOL group E-19), and the Brazilian CNPq through the grant PVE of the Ciencias Sem Fronteiras program. HS acknowledges funding via a JAEPre grant from the National Research Council of Spain. RFSA and FSB acknowledge financial support from FAPESB (Contract No. PNX 0006/2009) and by CNPQ (INCT-SC).