Enhancing synchronization criteria for fractional-order chaotic neural networks via intermittent control: an extended dissipativity approach

Saravanan Shanmugam; R. Vadivel; S. Sabarathinam; P. Hammachukiattikul; Nallappan Gunasekaran; Saravanan Shanmugam; R. Vadivel; S. Sabarathinam; P. Hammachukiattikul; Nallappan Gunasekaran

doi:10.3934/mmc.2025003

Mathematical Modelling and Control

2025, Volume 5, Issue 1: 31-47. doi: 10.3934/mmc.2025003

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Enhancing synchronization criteria for fractional-order chaotic neural networks via intermittent control: an extended dissipativity approach

1.
Center for Computational Biology, Easwari Engineering College, Chennai, Tamilnadu 600089, India
2.
Center for Research, SRM Institute of Science and Technology, Ramapuram, Chennai, Tamilnadu 600089, India
3.
Department of Mathematics, Faculty of Science and Technology, Phuket Rajabhat University, Phuket 83000, Thailand
4.
Laboratory of Complex Systems Modelling and Control, Faculty of Computer Science, National Research University, High School of Economics, Moscow 109028, Russia
5.
Eastern Michigan Joint College of Engineering, Beibu Gulf University, Qinzhou 535011, China

Received: 28 January 2024 Revised: 24 July 2024 Accepted: 02 September 2024 Published: 12 March 2025

In this paper, a recurrent intermittent control (RIC) for the synchronization of fractional-order chaotic neural networks (FOCNNs) is proposed in view of the extended dissipativity-based approach. Successively, standard linear matrix inequalites (LMIs)-based extended dissipative criteria are derived through differential inclusions and inequality mechanisms. Several sufficient conditions are obtained to ensure the synchronization of FOCNNs. Furthermore, RIC is generated to solve the synchronization problem for the considered FOCNNs. Based on the piecewise Lyapunov functional, this paper derives a exponentially stable criterion in connection with linear matrix inequalities using the Matlab toolbox. Extended dissipativity can be employed to precisely define $ L_2 $–$ L_{\infty} $, $ H_{\infty} $, passivity, and $ (Q, S, R) $-$ \vartheta $ dissipative performance. This is achieved by modifying the weighting matrices to achieve the desired performance level. The successful application of the stability criterion that was planned is demonstrated by the outcomes of the simulation.
- extended dissipativity,
- fractional-order neural networks,
- linear matrix inequality,
- intermittent control,
- synchronization
Citation: Saravanan Shanmugam, R. Vadivel, S. Sabarathinam, P. Hammachukiattikul, Nallappan Gunasekaran. Enhancing synchronization criteria for fractional-order chaotic neural networks via intermittent control: an extended dissipativity approach[J]. Mathematical Modelling and Control, 2025, 5(1): 31-47. doi: 10.3934/mmc.2025003

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Abstract

In this paper, a recurrent intermittent control (RIC) for the synchronization of fractional-order chaotic neural networks (FOCNNs) is proposed in view of the extended dissipativity-based approach. Successively, standard linear matrix inequalites (LMIs)-based extended dissipative criteria are derived through differential inclusions and inequality mechanisms. Several sufficient conditions are obtained to ensure the synchronization of FOCNNs. Furthermore, RIC is generated to solve the synchronization problem for the considered FOCNNs. Based on the piecewise Lyapunov functional, this paper derives a exponentially stable criterion in connection with linear matrix inequalities using the Matlab toolbox. Extended dissipativity can be employed to precisely define $ L_2 $–$ L_{\infty} $, $ H_{\infty} $, passivity, and $ (Q, S, R) $-$ \vartheta $ dissipative performance. This is achieved by modifying the weighting matrices to achieve the desired performance level. The successful application of the stability criterion that was planned is demonstrated by the outcomes of the simulation.

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