# Intermittent stickiness synchronization

## TL;DR

This paper investigates the phenomenon of Intermittent Stickiness Synchronization in high-dimensional Hamiltonian systems using FTLEs, revealing universal decay behaviors and rare long-term full synchronization events in mixed phase space.

## Contribution

It introduces a novel analysis of ISS using FTLEs, demonstrating universal decay exponents and the rarity of long-term full synchronization in complex systems.

## Key findings

- Full SS occurs when all FTLEs tend to zero over long times.
- Partial SS depends on system parameters and phase space dimension.
- Full SS can appear after very long times due to slow decay of correlations.

## Abstract

This work uses the statistical properties of Finite-Time Lyapunov Exponents (FTLEs) to investigate the Intermittent Stickiness Synchronization (ISS) observed in the mixed phase space of high-dimensional Hamiltonian systems. Full Stickiness Synchronization (SS) occurs when all FTLEs from a chaotic trajectory tend to zero for arbitrary long time-windows. This behavior is a consequence of the sticky motion close to regular structures which live in the high-dimensional phase space and affects all unstable directions proportionally by the same amount, generating a kind of collective motion. Partial SS occurs when at least one FTLE approaches to zero. Thus, distinct degrees of partial SS may occur, depending on the values of nonlinearity and coupling parameters, on the dimension of the phase space and on the number of positive FTLEs. Through filtering procedures used to precisely characterize the sticky motion, we are able to compute the algebraic decay exponents of the ISS and to obtain remarkable evidence about the existence of a universal behavior related to the decay of time correlations encoded in such exponents. In addition, we show that even though the probability to find full SS is small compared to partial SSs, the full SS may appear for very long times due to the slow algebraic decay of time correlations in mixed phase space. In this sense, observations of very late intermittence between chaotic motion and full SSs become rare events.