Chaos synchronization of canonically and Lie-algebraically deformed Henon-Heiles systems by active control

TL;DR

This paper demonstrates the synchronization of two chaotic Henon-Heiles systems deformed by different quantum space models using active control, providing a link between canonical and Lie-algebraic deformations.

Contribution

It introduces a method to synchronize chaos in deformed Henon-Heiles systems, connecting canonical and Lie-algebraic quantum space models through active control.

Findings

Successful numerical synchronization of the two models.

Derived active controllers at the phase-space level.

Established a direct link between different deformation models.

Abstract

Recently, there has been provided two chaotic models based on the twist-deformation of classical Henon-Heiles system. First of them has been constructed on the well-known, canonical space-time noncommutativity, while the second one on the Lie-algebraically type of quantum space, with two spatial directions commuting to classical time. In this article, we find the direct link between mentioned above systems, by synchronization both of them in the framework of active control method. Particularly, we derive at the canonical phase-space level the corresponding active controllers as well as we perform (as an example) the numerical synchronization of analyzed models.