# Proximity to explosive synchronization determines network collapse and recovery trajectories in neural and economic crises

## TL;DR

This paper shows how systems like the brain and stock markets can be predicted to collapse or recover based on their proximity to a physics phenomenon called explosive synchronization.

## Contribution

A physics-based framework is introduced to estimate a system's proximity to explosive synchronization, enabling prediction of collapse and recovery dynamics.

## Key findings

- Proximity to explosive synchronization predicts rapid collapse and slow recovery in systems like the brain and stock markets.
- The framework was validated using EEG data during anesthesia and stock market data during the 2008 crisis.
- Systems closer to first-order transitions show more instability and slower recovery.

## Abstract

Why do some systems collapse abruptly and recover slowly, while others remain resilient? We show that the difference depends on how close a system’s second-order phase transition is to the first-order (explosive) limit, quantified as explosive synchronization (ES) proximity. Incorporating this measure into conventional criticality analysis provides a way to predict a network’s behavior during crises. Using this approach, we demonstrate that the loss and recovery of consciousness under anesthesia, as well as the collapse and recovery of stock markets during the 2008 economic crisis, can be systematically predicted as either rapid or slow. This framework offers a unified, physics-based tool for anticipating transition trajectories across complex systems.

Complex systems such as the conscious brain and financial markets often operate near criticality, a regime that supports flexible and efficient function. When perturbed, however, rapid deviations from, and prolonged recovery to, criticality can severely disrupt these systems. The nature of such transitions depends on a system’s intrinsic phase transition type. Most systems in nature undergo continuous (second-order) transitions, but some approach a discontinuous, first-order transition known as explosive synchronization (ES). Systems nearer to first-order transitions are more unstable, losing criticality more rapidly and recovering more slowly. However, no existing method can directly determine from empirical data how close a system is to a first-order regime, limiting our ability to predict criticality transition patterns. Here, we introduce a physics-based framework that estimates a network’s ES proximity at the critical point. Using modified Stuart–Landau oscillator networks, we show that distinct critical dynamics emerge depending on the proximity to ES and that this measure predicts the temporal patterns of collapse and recovery under perturbations. We validated the generality of our computational findings with empirical data on network collapse and recovery, using human electroencephalogram recordings during general anesthesia and global stock market indices from 39 countries during the 2008 economic crisis. We demonstrated that rapid collapses and prolonged recoveries in both brain and stock market networks can be systematically predicted for neuronal and economic crises. These results provide crucial insights for designing resilient networks capable of withstanding perturbations and recovering quickly.