Izvestiya of Saratov University.

Physics

ISSN 1817-3020 (Print)
ISSN 2542-193X (Online)


For citation:

Illarionova E. D., Moskalenko O. I. Method of recurrent analysis for the generalized synchronization regime detection in different classes of dynamical systems. Izvestiya of Saratov University. Physics , 2025, vol. 25, iss. 3, pp. 288-294. DOI: 10.18500/1817-3020-2025-25-3-288-294, EDN: HDUENA

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
29.08.2025
Full text:
(downloads: 137)
Language: 
Russian
Article type: 
Article
UDC: 
517.9
EDN: 
HDUENA

Method of recurrent analysis for the generalized synchronization regime detection in different classes of dynamical systems

Autors: 
Illarionova Ekaterina Dmitrievna, Saratov State University
Moskalenko Ol’ga Igorevna, Saratov State University
Abstract: 

Background and Objectives: In this paper we study the possibility of quantitative determination of the boundary of the generalized synchronization regime in unidirectionally and mutually coupled systems with different attractor topologies by means of the recurrent analysis. Materials and Methods: As the systems under study we consider Lorenz and Rössler systems, as well as radiotechnical generators coupled unidirectionally and/or mutually. To evaluate the obtained data together with the recurrent analysis the spectrum of Lyapunov exponents or synchronization error were calculated for all the systems under study. Results: We have shown that for identical systems with detuned parameters the results of the method of recurrent analysis coincide with a high degree of accuracy with the values obtained using classical methods for the generalized synchronization regime detection, whereas for noindentical systems the proposed method demonstrates less accurate results. Conclusion: The method of calculation the recurrent diagrams allows us to determine the boundary of generalized synchronization in unidirectionally and mutually coupled systems with different attractor topology. The obtained results are in a good agreement with the results of calculation of the spectrum of Lyapunov exponents and synchronization error.

Acknowledgments: 
This work was supported by the Russian Science Foundation (project No. 24-22-00033, https://rscf.ru/project/24-22-00033/).
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Received: 
11.12.2024
Accepted: 
15.05.2025
Published: 
29.08.2025