# Controlling a complex system near its critical point via temporal correlations

## TL;DR

This paper investigates how complex systems near critical points can be controlled by leveraging temporal correlations, demonstrating a feedback mechanism that self-tunes systems like the Ising model, flocking, and neuronal networks to criticality.

## Contribution

It introduces a novel feedback control method based on autocorrelation functions to steer diverse complex systems toward their critical points.

## Key findings

- Feedback of autocorrelation functions can shift systems to criticality
- Universal properties enable broad applicability of the control method
- Validated on models: 2D Ising, 3D Vicsek, neuronal networks

## Abstract

A wide variety of complex systems exhibit large fluctuations both in space and time that often can be attributed to the presence of some kind of critical phenomena. Under such critical scenario it is well known that the properties of the correlation functions in space and time are two sides of the same coin. Here we test wether systems exhibiting a phase transition could self-tune to its critical point taking advantage of such correlation properties. We describe results in three models: the 2D Ising ferromagnetic model, the 3D Vicsek flocking model and a small-world neuronal network model. We illustrate how the feedback of the autocorrelation function of the order parameter fluctuations is able to shift the system towards its critical point. Since the results rely on universal properties they are expected to be relevant to a variety of other settings.