Recursive Tangential-Angular Operator as Analyzer of Synchronized Chaos

TL;DR

This paper introduces a new recursive tangential-angular operator for analyzing synchronization in chaotic oscillations, demonstrating its robustness and effectiveness in revealing attractor structure changes in coupled logistic maps.

Contribution

The paper presents a novel recursive tangential-angular operator method for analyzing synchronization in chaotic systems, capable of detecting attractor structure changes.

Findings

Method effectively reveals attractor structure changes.

Robust against noise and nonlinear distortions.

Validated on coupled logistic maps.

Abstract

A method for the quantitative analysis of the degree and parameters of synchronization of the chaotic oscillations in two coupled oscillators is proposed, which makes it possible to reveal a change in the structure of attractors. The proposed method is tested on a model system of two unidirectionally coupled logistic maps. It is shown that the method is robust with respect to both the presence of a low-intensity noise and a nonlinear distortion of the analyzed signal. Specific features of a rearranged structure of the attractor of a driven subsystem in the example under consideration have been studied.