Awaking and sleeping of a complex network

Authors:
R. López-Ruiz;Y. Moreno;A. F. Pacheco;S. Boccaletti;D. -U. Hwang
Affiliations:
Departament of Computer Science and BIFI, Faculty of Sciences, University of Zaragoza, 50009, Zaragoza, Spain;Departament of Theoretical Physics and BIFI, Faculty of Sciences, University of Zaragoza, 50009, Zaragoza, Spain;Departament of Theoretical Physics and BIFI, Faculty of Sciences, University of Zaragoza, 50009, Zaragoza, Spain;Istituto Nazionale di Ottica Applicata, Largo Enrico Fermi, 6, 50125-Firenze, Italy;Istituto Nazionale di Ottica Applicata, Largo Enrico Fermi, 6, 50125-Firenze, Italy
Venue:
Neural Networks
Year:
2007

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Abstract

A network with a logistic-like local dynamics is considered. We implement a mean-field multiplicative coupling among first-neighbor nodes. When the coupling parameter is small, the dynamics is dissipated and there is no activity: the network is turned off. For a critical value of the coupling, a non-null stable synchronized state, which represents a turned on network, emerges. This global bifurcation is independent of the network topology. We characterize the bistability of the system by studying how to perform the transition, which is now topology dependent, from the active state to that with no activity, for the particular case of a scale-free network. This could be a naive model for the wakening and sleeping of a brain-like system, i.e., a multi-component system with two different dynamical behaviors.