Percolation on Networks with Antagonistic and Dependent Interactions

TL;DR

This paper investigates the dynamics of two interacting networks with antagonistic and dependent links, revealing continuous phase transitions, enhanced robustness, and oscillatory behaviors under certain conditions, advancing understanding of complex real-world systems.

Contribution

It introduces a model of two networks with antagonistic and dependent interactions, showing novel continuous phase transitions and oscillatory phenomena not seen in traditional interdependent networks.

Findings

Networks are more robust against random attacks compared to isolated networks.

Oscillations in giant connected components occur under high dependency and antagonism.

Phase transitions are continuous, unlike the first-order transitions in interdependent networks.

Abstract

Drawing inspiration from real world interacting systems we study a system consisting of two networks that exhibit antagonistic and dependent interactions. By antagonistic and dependent interactions, we mean, that a proportion of functional nodes in a network cause failure of nodes in the other, while failure of nodes in the other results in failure of links in the first. As opposed to interdependent networks, which can exhibit first order phase transitions, we find that the phase transitions in such networks are continuous. Our analysis shows that, compared to an isolated network, the system is more robust against random attacks. Surprisingly, we observe a region in the parameter space where the giant connected components of both networks start oscillating. Furthermore, we find that for Erdos-Renyi and scale free networks the system oscillates only when the dependency and antagonism between the two networks is very high. We believe that this study can further our understanding of real world interacting systems.