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Adaptive synchronization in the complex heterogeneous networks of Hindmarsh–Rose neurons. / Semenov, Danila M.; Fradkov, Alexander L.

In: Chaos, Solitons and Fractals, Vol. 150, 111170, 01.09.2021.

Research output: Contribution to journal › Article › peer-review

Harvard

Semenov, DM & Fradkov, AL 2021, 'Adaptive synchronization in the complex heterogeneous networks of Hindmarsh–Rose neurons', Chaos, Solitons and Fractals, vol. 150, 111170. https://doi.org/10.1016/j.chaos.2021.111170

APA

Semenov, D. M., & Fradkov, A. L. (2021). Adaptive synchronization in the complex heterogeneous networks of Hindmarsh–Rose neurons. Chaos, Solitons and Fractals, 150, [111170]. https://doi.org/10.1016/j.chaos.2021.111170

Vancouver

Semenov DM, Fradkov AL. Adaptive synchronization in the complex heterogeneous networks of Hindmarsh–Rose neurons. Chaos, Solitons and Fractals. 2021 Sep 1;150. 111170. https://doi.org/10.1016/j.chaos.2021.111170

Author

Semenov, Danila M. ; Fradkov, Alexander L. / Adaptive synchronization in the complex heterogeneous networks of Hindmarsh–Rose neurons. In: Chaos, Solitons and Fractals. 2021 ; Vol. 150.

BibTeX

@article{146d9a4271a74791bcffffcfc3bc9b36,
title = "Adaptive synchronization in the complex heterogeneous networks of Hindmarsh–Rose neurons",
abstract = "This paper is devoted to the adaptive synchronization problem in the heterogeneous Hindmarsh–Rose neuronal networks. Heterogeneity is a natural property of biological neuronal networks, as each neuron has its own physiological characteristics, which may differ from other neurons within the population. Therefore, the study of the effect of heterogeneity on the synchronization in the biological neuronal network is an important problem. In order to solve this problem, the ultimate boundedness of the network trajectories is established, and also the limit set is defined for these trajectories. Based on the boundedness analysis and the Speed Gradient method, the adaptive algorithm for adjusting the coupling strength is developed. It is proved mathematically that the developed algorithm provides synchronization in the network under study. The obtained theoretical results are confirmed by the simulations.",
keywords = "Adaptive control, Hindmarsh–Rose model, Neural dynamics, Speed-gradient method, Synchronization, Ultimate boundedness, Hindmarsh-Rose model, STATES, CHAOTIC SYSTEMS, CONSENSUS, MODEL",
author = "Semenov, {Danila M.} and Fradkov, {Alexander L.}",
note = "Publisher Copyright: {\textcopyright} 2021 Elsevier Ltd",
year = "2021",
month = sep,
day = "1",
doi = "10.1016/j.chaos.2021.111170",
language = "English",
volume = "150",
journal = "Chaos, Solitons and Fractals",
issn = "0960-0779",
publisher = "Elsevier",

}

RIS

TY - JOUR

T1 - Adaptive synchronization in the complex heterogeneous networks of Hindmarsh–Rose neurons

AU - Semenov, Danila M.

AU - Fradkov, Alexander L.

N1 - Publisher Copyright: © 2021 Elsevier Ltd

PY - 2021/9/1

Y1 - 2021/9/1

N2 - This paper is devoted to the adaptive synchronization problem in the heterogeneous Hindmarsh–Rose neuronal networks. Heterogeneity is a natural property of biological neuronal networks, as each neuron has its own physiological characteristics, which may differ from other neurons within the population. Therefore, the study of the effect of heterogeneity on the synchronization in the biological neuronal network is an important problem. In order to solve this problem, the ultimate boundedness of the network trajectories is established, and also the limit set is defined for these trajectories. Based on the boundedness analysis and the Speed Gradient method, the adaptive algorithm for adjusting the coupling strength is developed. It is proved mathematically that the developed algorithm provides synchronization in the network under study. The obtained theoretical results are confirmed by the simulations.

AB - This paper is devoted to the adaptive synchronization problem in the heterogeneous Hindmarsh–Rose neuronal networks. Heterogeneity is a natural property of biological neuronal networks, as each neuron has its own physiological characteristics, which may differ from other neurons within the population. Therefore, the study of the effect of heterogeneity on the synchronization in the biological neuronal network is an important problem. In order to solve this problem, the ultimate boundedness of the network trajectories is established, and also the limit set is defined for these trajectories. Based on the boundedness analysis and the Speed Gradient method, the adaptive algorithm for adjusting the coupling strength is developed. It is proved mathematically that the developed algorithm provides synchronization in the network under study. The obtained theoretical results are confirmed by the simulations.

KW - Adaptive control

KW - Hindmarsh–Rose model

KW - Neural dynamics

KW - Speed-gradient method

KW - Synchronization

KW - Ultimate boundedness

KW - Hindmarsh-Rose model

KW - STATES

KW - CHAOTIC SYSTEMS

KW - CONSENSUS

KW - MODEL

UR - http://www.scopus.com/inward/record.url?scp=85109030382&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/1e7bcf06-c73f-3cb9-94bf-e218a41c338a/

U2 - 10.1016/j.chaos.2021.111170

DO - 10.1016/j.chaos.2021.111170

M3 - Article

AN - SCOPUS:85109030382

VL - 150

JO - Chaos, Solitons and Fractals

JF - Chaos, Solitons and Fractals

SN - 0960-0779

M1 - 111170

ER -

ID: 87327891