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

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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.

About the authors

Ekaterina Dmitrievna Illarionova

Saratov State University

ORCID iD: 0000-0003-1912-863X
410012, Russia, Saratov, Astrakhanskaya street, 83

Ol’ga Igorevna Moskalenko

Saratov State University

ORCID iD: 0000-0001-5727-5169
SPIN-code: 7186-3695
Scopus Author ID: 10038769200
ResearcherId: D-4420-2011
410012, Russia, Saratov, Astrakhanskaya street, 83

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