ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

For citation:

Moskalenko O. I., Evstifeev E. V. On existence of multistability near the boundary of generalized synchronization in unidirectionally coupled systems with complex topology of attractor. Izvestiya VUZ. Applied Nonlinear Dynamics, 2022, vol. 30, iss. 6, pp. 676-684. DOI: 10.18500/0869-6632-003013, EDN: LSEQWO

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Language: 
Russian
Heading: 
Bifurcation in Dynamical Systems. Deterministic Chaos. Quantum Chaos.
Article type: 
Article
UDC: 
517.9
DOI: 
10.18500/0869-6632-003013
EDN: 
LSEQWO

On existence of multistability near the boundary of generalized synchronization in unidirectionally coupled systems with complex topology of attractor

Autors: 
Moskalenko Olga Igorevna, Saratov State University
Evstifeev Evgeniy Valentinovich, Saratov State University
Abstract: 

Aim of this work is to study the possibility of existence of multistability near the boundary of generalized synchronization in systems with complex attractor topology. Unidirectionally coupled Lorentz systems have been chosen as an object of study, and a modified auxiliary system method has been used to detect the presence of the synchronous regime. Result of the work is a proof of the presence of multistability near the boundary of generalized synchronization in unidirectionally coupled systems with a complex topology of attractor. For this purpose, the basins of attraction of the synchronous and asynchronous states of interacting Lorenz systems have been obtained for the value of the coupling parameter corresponding to the realization of the intermittent generalized synchronization regime in the system under study, and the dependence of the multistability measure on the value of the coupling parameter has also been calculated. It is shown that in the regime of intermittent generalized synchronization the measure of multistability turns out to be positive, which is an additional confirmation of the presence of multistability in this case.

Key words: 
generalized synchronization
multistability
systems with complex topology of attractor
intermittency
auxiliary system approach
Acknowledgments: 
This work was financially supported by the Grant Council of the President of the Russian Federation for the state support of young Russian scientists — doctors of sciences (project No. MD-18.2022.1.2)
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Received: 
03.06.2022
Accepted: 
06.07.2022
Available online: 
14.10.2022
Published: 
30.11.2022
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