Competition of simple and complex adoption on interdependent networks

TL;DR

This paper investigates how the interplay between complex threshold and simple SIS adoption models on interconnected networks affects transition points and the nature of adoption phases, revealing that coupling modifies thresholds and can induce new transition types.

Contribution

It introduces a coupled model of complex and simple adoption processes on interdependent networks, analyzing how interlayer connectivity influences transition thresholds and behaviors.

Findings

Transition points are shifted by interlayer coupling.

The nature of transitions can change from discontinuous to continuous.

A new sudden drop transition appears in the SIS layer.

Abstract

We consider the competition of two mechanisms for adoption processes: a so-called complex threshold dynamics and a simple Susceptible-Infected-Susceptible (SIS) model. Separately, these mechanisms lead, respectively, to first order and continuous transitions between non-adoption and adoption phases. We consider two interconnected layers. While all nodes on the first layer follow the complex adoption process, all nodes on the second layer follow the simple adoption process. Coupling between the two adoption processes occurs as a result of the inclusion of some additional interconnections between layers. We find that the transition points and also the nature of the transitions are modified in the coupled dynamics. In the complex adoption layer, the critical threshold required for extension of adoption increases with interlayer connectivity whereas in the case of an isolated single network it would decrease with average connectivity. In addition, the transition can become continuous depending on the detailed inter and intralayer connectivities. In the SIS layer, any interlayer connectivity leads to the extension of the adopter phase. Besides, a new transition appears as as sudden drop of the fraction of adopters in the SIS layer. The main numerical findings are described by a mean-field type analytical approach appropriately developed for the threshold-SIS coupled system.