# Optimal interdependence enhances robustness of complex systems

## TL;DR

This paper demonstrates that increasing interdependence between coupled networks can enhance their robustness by creating stable activity attractors, contrary to the usual association of interdependence with fragility.

## Contribution

It introduces a novel perspective showing that optimal interdependence can promote robustness in interconnected dynamical systems, supported by analysis of coupled network dynamics.

## Key findings

- System-wide persistence of activity at optimal interdependence levels
- Formation of stable activity attractors ('islands') in the global dynamics
- Counterintuitive robustness enhancement through interdependence

## Abstract

While interdependent systems have usually been associated with increased fragility, we show that strengthening the interdependence between dynamical processes on different networks can make them more robust. By coupling the dynamics of networks that in isolation exhibit catastrophic collapse with extinction of nodal activity, we demonstrate system-wide persistence of activity for an optimal range of interdependence between the networks. This is related to the appearance of attractors of the global dynamics comprising disjoint sets ("islands") of stable activity.