Chaos in Small-World Networks

TL;DR

This paper investigates how nonlinear interactions and time delays influence the dynamics of small-world networks, revealing chaotic behavior and scale-dependent properties through simulations and analysis.

Contribution

It introduces a nonlinear small-world network model incorporating time delay, providing new insights into the chaotic dynamics and scale-dependent behaviors of such networks.

Findings

Chaotic features emerge under strong nonlinear interactions or large length scales.

Time delay significantly affects critical length and response time.

Small-world networks exhibit different behaviors at different scales.

Abstract

A nonlinear small-world network model has been presented to investigate the effect of nonlinear interaction and time delay on the dynamic properties of small-world networks. Both numerical simulations and analytical analysis for networks with time delay and nonlinear interaction show chaotic features in the system response when nonlinear interaction is strong enough or the length scale is large enough. In addition, the small-world system may behave very differently on different scales. Time-delay parameter also has a very strong effect on properties such as the critical length and response time of small-world networks.