# Synchronization, phase slips and coherent structures in area-preserving maps

## TL;DR

This paper investigates synchronization phenomena in coupled area-preserving maps, revealing how phase space structures influence synchronization times and the effects of perturbations on basin size and synchronization behavior.

## Contribution

It provides new insights into how regular and chaotic structures affect synchronization and introduces parameter perturbations to enhance synchronization in Hamiltonian systems.

## Key findings

- Complete synchronization occurs at certain nonlinear parameters.
- Synchronization time distribution shifts from power law to exponential with perturbations.
- Perturbations increase the basin of synchronization and reduce synchronization times.

## Abstract

The problem of synchronization of coupled Hamiltonian systems exhibits interesting features due to the non-uniform or mixed nature (regular and chaotic) of the phase space. We study these features by investigating the synchronization of unidirectionally coupled area-preserving maps coupled by the Pecora-Carroll method. We find that coupled standard maps show complete synchronization for values of the nonlinearity parameter at which regular structures are still present in phase space. The distribution of synchronization times has a power law tail indicating long synchronization times for at least some of the synchronizing trajectories. With the introduction of coherent structures using parameter perturbation in the system, this distribution crosses over to exponential behavior, indicating shorter synchronization times, and the number of initial conditions which synchronize increases significantly, indicating an enhancement in the basin of synchronization. On the other hand, coupled blinking vortex maps display both phase synchronization and phase slips, depending on the location of the initial conditions. We discuss the implication of our results.