Controlling synchronization in coupled area-preserving maps using stickiness

TL;DR

This paper explores methods to control synchronization timing in coupled area-preserving maps by leveraging stickiness near regular islands, using controlled kicks and parameter perturbations.

Contribution

It introduces novel numerical procedures to delay or expedite synchronization in coupled maps by exploiting phase space stickiness.

Findings

Controlled kicking can delay synchronization by keeping trajectories away from traps.

Parameter perturbation can rapidly induce synchronization in chaotic trajectories.

Methods have limitations depending on phase space structure.

Abstract

Unidirectionally coupled area-preserving maps with a mixed phase space may show identical synchronization in the sticky neighborhood of the regular islands. We use this fact to devise numerical procedures to control (delay and expedite) the process of synchronization in two standard maps coupled under the Pecora-Carroll coupling scheme. The delay method is based on controlled kicking of trajectories away from synchronization traps for as long as necessary. The method to expedite the process is achieved by a parameter perturbation technique which rapidly drives the chaotic trajectories to synchronization traps in the sticky neighborhoods of regular islands. We also discuss the limitations of these methods.