# Comprehending deterministic and stochastic occasional uncoupling induced synchronizations through each other

## TL;DR

This paper investigates how stochastic and deterministic occasional uncoupling methods induce synchronization in chaotic flows, introducing a hybrid approach called transient stochastic uncoupling that outperforms existing schemes.

## Contribution

It introduces the transient stochastic uncoupling method, combining deterministic and stochastic uncoupling, and demonstrates its superior effectiveness in synchronizing chaotic systems.

## Key findings

- Transient stochastic uncoupling surpasses stochastic on-off coupling in efficiency.
- Autocorrelation of the response system's time series predicts successful deterministic uncoupling.
- Local indicators of contraction are not reliable for finding optimal coupling regions.

## Abstract

In this paper, we numerically study the stochastic and the deterministic occasional uncoupling methods of effecting identical synchronized states in low dimensional, dissipative, diffusively coupled, chaotic flows that are otherwise not synchronized when continuously coupled at the same coupling strength parameter. In the process of our attempt to understand the mechanisms behind the success of the occasional uncoupling schemes, we devise a hybrid between the transient uncoupling and the stochastic on-off coupling, and aptly name it the transient stochastic uncoupling---yet another stochastic occasional uncoupling method. Our subsequent investigation on the transient stochastic uncoupling allows us to surpass the effectiveness of the stochastic on-off coupling with very fast on-off switching rate. Additionally, through the transient stochastic uncoupling, we establish that the indicators quantifying the local contracting dynamics in the corresponding transverse manifold are generally not useful in finding the optimal coupling region of the phase space in the case of the deterministic transient uncoupling. In fact, we highlight that the autocorrelation function---a non-local indicator of the dynamics---of the corresponding response system's chaotic time-series dictates when the deterministic uncoupling could be successful. We illustrate all our heuristic results using a few well-known examples of diffusively coupled chaotic oscillators.