Phase Synchronization and invariant measures in sinusoidally perturbed chaotic systems

TL;DR

This paper investigates phase synchronization in sinusoidally perturbed chaotic systems, revealing the existence of invariant measures and transformations related to the perturbation frequency, supported by experimental and numerical analysis of Chua's circuit.

Contribution

It introduces a novel perspective on phase synchronization using stroboscopic maps and characterizes the types of transformations present in perturbed chaotic systems.

Findings

Phase synchronization correlates with invariant measures of the perturbation.

Non-transient transformations can be infinite in number during synchronization.

Absence of synchronization involves only transitive or finite non-transitive transformations.

Abstract

We show that, in periodically perturbed chaotic systems, Phase Synchronization appears, associated to a special type of stroboscopic map, in which not only averages quantities are equal to invariants of the perturbation, the angular frequency, but also it exists a very large number of non-transient transformations, possibly infinity. In cases where there is not phase synchronization there is either only transitive transformations on the attractor, or a finite number of non-transitive transformations. We base our statements in experimental and numerical results from the sinusoidally perturbed Chua's circuit.