Drastic disorder-induced reduction of signal amplification in scale-free networks.

Ricardo Chacón,Pedro J Martínez

doi:10.1103/physreve.92.012821

Abstract

Understanding information transmission across a network is a fundamental task for controlling and manipulating both biological and manmade information-processing systems. Here we show how topological resonant-like amplification effects in scale-free networks of signaling devices are drastically reduced when phase disorder in the external signals is considered. This is demonstrated theoretically by means of a starlike network of overdamped bistable systems, and confirmed numerically by simulations of scale-free networks of such systems. The taming effect of the phase disorder is found to be sensitive to the amplification's strength, while the topology-induced amplification mechanism is robust against this kind of quenched disorder in the sense that it does not significantly change the values of the coupling strength where amplification is maximum in its absence.

Highlights

During the last decade, there has been considerable interest in a class of real-world networks known as scale-free networks [1,2] which have the property that the degrees, κ, of the node follow a scale-free power-law distribution (P (κ) ∼ κ−γ,γ ∈ [2,3])
The taming effect of the phase disorder is found to be sensitive to the amplification’s strength, while the topology-induced amplification mechanism is robust against this kind of quenched disorder in the sense that it does not significantly change the values of the coupling strength where amplification is maximum in its absence
We have shown through the example of a network of overdamped bistable systems that phase disorder in the external signals strongly reduces topology-induced signal amplification in scale-free networks

Summary

INTRODUCTION

There has been considerable interest in a class of real-world networks known as scale-free networks [1,2] which have the property that the degrees, κ, of the node follow a scale-free power-law distribution (P (κ) ∼ κ−γ ,γ ∈ [2,3]). Of special relevance is the propagation and enhancement of resonant collective behavior across a network due to the application of weak external signals because of its importance in both biological and manmade information-processing systems In this regard, it has been recently studied the amplification of the response to weak external signals in networks of bistable signaling devices [14,15,16,17]. We study the interplay between heterogeneous connectivity and quenched spatial and temporal disorder in random scale-free networks of signaling devices through the example of a deterministic overdamped bistable system This system is sufficiently simple to obtain analytical predictions while retaining the universal characteristic of a two-state system.

STARLIKE NETWORK

BARABA SI-ALBERT NETWORK

CONCLUSION