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

TL;DR

This paper investigates how information is transmitted between complex networks exhibiting 1/f noise, revealing conditions under which maximal information transfer occurs based on their spectral properties and generalized fluctuation-dissipation relations.

Contribution

It introduces a generalized fluctuation-dissipation framework to analyze information transfer in complex networks with 1/f noise, identifying key spectral conditions for maximal information transport.

Findings

Maximal information transfer occurs when both networks exhibit ideal 1/f-noise.

Network response depends on the spectral index ; response occurs if <2.

Inheritance of relaxation properties occurs when  of perturbing network is less than that of the system.

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.