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

For citation:

Illarionova E. D., Moskalenko O. I. Multistability near the boundary of noise-induced synchronization in ensembles of uncoupled chaotic systems. Izvestiya VUZ. Applied Nonlinear Dynamics, 2023, vol. 31, iss. 5, pp. 566-574. DOI: 10.18500/0869-6632-003061, EDN: KVJVOV

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Language: 
Russian
Heading: 
Bifurcation in Dynamical Systems. Deterministic Chaos. Quantum Chaos.
Article type: 
Article
UDC: 
517.9
DOI: 
10.18500/0869-6632-003061
EDN: 
KVJVOV

Multistability near the boundary of noise-induced synchronization in ensembles of uncoupled chaotic systems

Autors: 
Illarionova Ekaterina Dmitrievna, Saratov State University
Moskalenko Olga Igorevna, Saratov State University
Abstract: 

The aim of this work is to study the possibility of the existence of multistability near the boundary of noise-induced synchronization in chaotic continuous and discrete systems. Ensembles of uncoupled Lorenz systems and logistic maps being under influence of a common source of white noise have been chosen as an object under study.

Methods. The noise-induced synchronization regime detection has been performed by means of direct comparison of the system states being under influence of the common noise source and by calculation of the synchronization error. To determine the presence of multistability near the boundary of this regime, the multistability measure has been calculated and its dependence on the noise intensity has been obtained. In addition, for fixed moments of time, the basins of attraction of the synchronous and asynchronous regimes have been received for one of the systems driven by noise for fixed initial conditions of the other system.

The result of the work is a proof of the presence of multistability near the boundary of noise-induced synchronization.

Conclusion. It is shown that the regime of intermittent noise-induced synchronization, as well as the regime of intermittent generalized synchronization, is characterized by multistability, which manifests itself in this case as the existence in the same time interval of the synchronous behavior in one pair of systems being under influence of a common noise source, whereas in the other pair the asynchronous behavior is observed. The found effect is typical for both flow systems and discrete maps being under influence of a common noise source. It can find an application in the information and telecommunication systems for improvement the methods for secure information transmission based on the phenomenon of chaotic synchronization.

Key words: 
noise-induced synchronization
generalized synchronization
multistability
white noise
intermittency
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 N. MD-18.2022.1.2)
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Received: 
20.06.2023
Accepted: 
13.07.2023
Available online: 
14.09.2023
Published: 
29.09.2023
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