# Dynamics of Tipping Cascades on Complex Networks

## TL;DR

This paper explores how different network topologies influence the spread of tipping points in complex systems, using simulations on various network models and real-world data, revealing that clustering and spatial organization increase vulnerability.

## Contribution

It introduces a comprehensive analysis of how network structure affects tipping cascades, combining model simulations with real-world data from the Amazon rainforest.

## Key findings

- Clustering and spatial organization increase network vulnerability.
- Real-world networks like the Amazon are more susceptible to cascades.
- Network topology can inform system design to enhance robustness.

## Abstract

Tipping points occur in diverse systems in various disciplines such as ecology, climate science, economy or engineering. Tipping points are critical thresholds in system parameters or state variables at which a tiny perturbation can lead to a qualitative change of the system. Many systems with tipping points can be modeled as networks of coupled multistable subsystems, e.g. coupled patches of vegetation, connected lakes, interacting climate tipping elements or multiscale infrastructure systems. In such networks, tipping events in one subsystem are able to induce tipping cascades via domino effects. Here, we investigate the effects of network topology on the occurrence of such cascades. Numerical cascade simulations with a conceptual dynamical model for tipping points are conducted on Erd\H{o}s-R\'enyi, Watts-Strogatz and Barab\'asi-Albert networks. Additionally, we generate more realistic networks using data from moisture-recycling simulations of the Amazon rainforest and compare the results to those obtained for the model networks. We furthermore use a directed configuration model and a stochastic block model which preserve certain topological properties of the Amazon network to understand which of these properties are responsible for its increased vulnerability. We find that clustering and spatial organization increase the vulnerability of networks and can lead to tipping of the whole network. These results could be useful to evaluate which systems are vulnerable or robust due to their network topology and might help to design or manage systems accordingly.