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arXiv · 1112.5553

Transmission of Information between Complex Networks: 1/f-Resonance

Gerardo Aquino·Mauro Bologna·Paolo Grigolini·Bruce J. West
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Abstract

We study the transport of information between two complex networks with similar properties. Both networks generate non-Poisson renewal fluctuations with a power-law spectrum 1/f^(3-\mu), the case \mu= 2 corresponding to ideal 1/f-noise. We denote by \mu_S and \mu_P the power-law indexes of the network "system" of interest S and the perturbing network P respectively. By adopting a generalized fluctuation-dissipation theorem (FDT) we show that the ideal condition of 1/f-noise for both networks corresponds to maximal information transport. We prove that to make the network S respond when \mu_S < 2 we have to set the condition \mu_P < 2. In the latter case, if \mu_P < \mu_S, the system S inherits the relaxation properties of the perturbing network. In the case where \mu_P > 2, no response and no information transmission occurs in the long-time limit. We consider two possible generalizations of the fluctuation-dissipation theorem and show that both lead to maximal information transport in the condition of 1/f-noise.

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Gerardo Aquino, Mauro Bologna, Paolo Grigolini, Bruce J. West. 2011-12-23. Transmission of Information between Complex Networks: 1/f-Resonance. https://doi.org/10.1103/physreve.83.051130

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