NETWORKS AND 1/f NOISE

Abstract

Complex networks form one of the most challenging areas of modern research overarching the traditional scientific disciplines. Of particular importance is the manner in which information is shuttled back and forth between such networks, and whether or not there exists general principles that guide the flow of information. Herein, we identify Wiener's rule, which conjectures how information is transfered in an information-dominated process. Moreover, we show that this rule is a consequence of the Principle of Complexity Management (PCM) that determines the information exchange between complex networks. A consequence of the PCM is that the maximum information transfer occurs at a 1/f noise resonance. The information transfer between two complex networks is also determined by direct numerical calculation of a master equation model of network dynamics using interacting two-state elements, the decision-making model (DMM). The DMM generates phase transitions and on a two-dimensional lattice, reduces to the Ising model in an appropriate limit. The computations using the DMM suggest that the inverse power laws of links and survival probability are not necessarily related.