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

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Shabunin A. V. Neural network as an indicator of connectivity in an ensemble of chaotic systems. Izvestiya VUZ. Applied Nonlinear Dynamics, 2026, vol. 34, iss. 2, pp. 331-344. DOI: 10.18500/0869-6632-003210, EDN: TRPSXT

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Language: 
Russian
Heading: 
Nonlinear Dynamics and Neuroscience
Article type: 
Article
UDC: 
517.9
DOI: 
10.18500/0869-6632-003210
EDN: 
TRPSXT

Neural network as an indicator of connectivity in an ensemble of chaotic systems

Autors: 
Shabunin Aleksej Vladimirovich, Saratov State University
Abstract: 

The purpose of this work is development and research of an algorithm for determining the structure of coupling of an ensemble of chaotic systems under conditions of external noise.

The method is based on the Granger causality approach and the use of artificial direct propagation neural networks trained with regularization.

Results. We have developed a method to identify the structure of couplings of a network of chaotic maps, which is based on the Granger causality principle and artificial neural networks. It represents a modification of the previously proposed algorithm and allows us to find the connectivity of the ensemble as a whole by a single pass of the network training. The algorithm has shown its effectiveness for an example of a small ensemble of non-identical maps with linear couplings. It keeps to work at presences of weak external noise, thogh the
accuracy of the method deteriorates with the noise intensity.

Discussion. The method has demonstrated its effectiveness for simple mathematical models, including in the presence of noise. However, its effectiveness at larger noise intensity requires additional statistical processing methods. It is also interesting to consider how it works for other types of coupings.
 

Key words: 
dynamical chaos
artificial neural networks
ensembles of maps
couplings structure identification
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Received: 
12.12.2025
Accepted: 
04.01.2026
Available online: 
27.01.2026
Published: 
31.03.2026
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