Cluster synchronization of coupled complex-valued neural networks with leakage and time-varying delays in finite-time

N. Jayanthi; R. Santhakumari; Grienggrai Rajchakit; Nattakan Boonsatit; Anuwat Jirawattanapanit; N. Jayanthi; R. Santhakumari; Grienggrai Rajchakit; Nattakan Boonsatit; Anuwat Jirawattanapanit

doi:10.3934/math.2023104

AIMS Mathematics

2023, Volume 8, Issue 1: 2018-2043. doi: 10.3934/math.2023104

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Research article Special Issues

Cluster synchronization of coupled complex-valued neural networks with leakage and time-varying delays in finite-time

1.
Government Arts College, Coimbatore, India
2.
Sri Ramakrishna College of Arts and Science, Coimbatore, India
3.
Department of Mathematics, Faculty of Science, Maejo University, Chiang Mai 50290, Thailand
4.
Faculty of Science and Technology, Rajamangala University of Technology Suvarnabhumi, Thailand
5.
Department of Mathematics, Faculty of Science, Phuket Rajabhat University (PKRU), Thailand

Received: 31 August 2022 Revised: 11 October 2022 Accepted: 14 October 2022 Published: 26 October 2022
MSC : 93D05, 93D40, 34D06, 92B20, 93C43

In cluster synchronization (CS), the constituents (i.e., multiple agents) are grouped into a number of clusters in accordance with a function of nodes pertaining to a network structure. By designing an appropriate algorithm, the cluster can be manipulated to attain synchronization with respect to a certain value or an isolated node. Moreover, the synchronization values among various clusters vary. The main aim of this study is to investigate the asymptotic and CS problem of coupled delayed complex-valued neural network (CCVNN) models along with leakage delay in finite-time (FT). In this paper, we describe several sufficient conditions for asymptotic synchronization by utilizing the Lyapunov theory for differential systems and the Filippov regularization framework for the realization of finite-time synchronization of CCVNNs with leakage delay. We also propose sufficient conditions for CS of the system under scrutiny. A synchronization algorithm is developed to indicate the usefulness of the theoretical results in case studies.
- complex-valued neural networks,
- leakage delay,
- time-varying delay,
- cluster synchronization,
- finite-time synchronization,
- Lyapunov stability theory
Citation: N. Jayanthi, R. Santhakumari, Grienggrai Rajchakit, Nattakan Boonsatit, Anuwat Jirawattanapanit. Cluster synchronization of coupled complex-valued neural networks with leakage and time-varying delays in finite-time[J]. AIMS Mathematics, 2023, 8(1): 2018-2043. doi: 10.3934/math.2023104

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Abstract

In cluster synchronization (CS), the constituents (i.e., multiple agents) are grouped into a number of clusters in accordance with a function of nodes pertaining to a network structure. By designing an appropriate algorithm, the cluster can be manipulated to attain synchronization with respect to a certain value or an isolated node. Moreover, the synchronization values among various clusters vary. The main aim of this study is to investigate the asymptotic and CS problem of coupled delayed complex-valued neural network (CCVNN) models along with leakage delay in finite-time (FT). In this paper, we describe several sufficient conditions for asymptotic synchronization by utilizing the Lyapunov theory for differential systems and the Filippov regularization framework for the realization of finite-time synchronization of CCVNNs with leakage delay. We also propose sufficient conditions for CS of the system under scrutiny. A synchronization algorithm is developed to indicate the usefulness of the theoretical results in case studies.

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