# Dynamic interdependence and competition in multilayer networks

## TL;DR

This paper introduces a general framework for modeling interdependence and competition in dynamic multilayer networks, revealing complex behaviors like explosive transitions, hysteresis, and chaos in interconnected systems.

## Contribution

It develops a novel, broadly applicable dynamic dependency framework and applies it to oscillator networks and epidemic models, uncovering new phenomena.

## Key findings

- Discovered explosive synchronization transitions.
- Identified hysteresis and multi-stability in interdependent systems.
- Revealed chaotic behavior in complex network interactions.

## Abstract

From critical infrastructure, to physiology and the human brain, complex systems rarely occur in isolation. Instead, the functioning of nodes in one system often promotes or suppresses the functioning of nodes in another. Despite advances in structural interdependence, modeling interdependence and other interactions between dynamic systems has proven elusive. Here we define a broadly applicable dynamic dependency link and develop a general framework for interdependent and competitive interactions between general dynamic systems. We apply our framework to studying interdependent and competitive synchronization in multi-layer oscillator networks and cooperative/competitive contagions in an epidemic model. Using a mean-field theory which we verify numerically, we find explosive transitions and rich behavior which is absent in percolation models including hysteresis, multi-stability and chaos. The framework presented here provides a powerful new way to model and understand many of the interacting complex systems which surround us.