Controlling the spreading in small-world networks

TL;DR

This paper investigates how to control the spread of diseases or failures in small-world networks by analyzing bifurcations and proposing a stabilization method for spreading behaviors.

Contribution

It introduces a control technique to stabilize periodic spreading behavior in small-world networks modeled with nonlinear dynamics.

Findings

Short-cut adding probability p influences bifurcation behavior.

A control method stabilizes spreading to a steady state.

Bifurcation analysis reveals critical parameters for spreading control.

Abstract

The spreading (propagation) of diseases, viruses, and disasters such as power blackout through a huge-scale and complex network is one of the most concerned issues today. In this paper, we study the control of such spreading in a nonlinear spreading model of small-world networks. We found that the short-cut adding probability $p$ in the N-W model \cite{N-W:1999} of small-world networks determines the Hopf bifurcation and other bifurcating behaviors in the proposed model. We further show a control technique that stabilize a periodic spreading behavior onto a stable equilibrium over the proposed model of small-world networks.