Effect analysis of pinning and impulsive selection for finite-time synchronization of delayed complex-valued neural networks

Shuang Liu; Tianwei Xu; Qingyun Wang; Shuang Liu; Tianwei Xu; Qingyun Wang

doi:10.3934/era.2025081

Electronic Research Archive

2025, Volume 33, Issue 3: 1792-1811. doi: 10.3934/era.2025081

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Effect analysis of pinning and impulsive selection for finite-time synchronization of delayed complex-valued neural networks

1.
Shanghai Engineering Research Center of Physical Vapor Deposition (PVD) Superhard Coating and Equipment, Shanghai Institute of Technology, Shanghai 201418, China
2.
Department of Dynamics and Control, Beihang University, Beijing 100191, China

Received: 19 December 2024 Revised: 19 February 2025 Accepted: 11 March 2025 Published: 27 March 2025

We explored the phenomenon of finite-time synchronization for coupled complex-valued neural networks that were subject to mixed-variable delays. To address this challenge, an impulsive pinning control strategy was proposed. The method presented entailed the dynamic adjustment of specific nodes at distinct impulsive intervals, contingent upon the magnitude of the errors observed in those nodes. Furthermore, an enhanced technique utilizing the sign function was employed to simultaneously manage the real and imaginary components of the complex-valued neural networks. By applying finite-time stability theorems and utilizing complex-valued inequalities, sufficient conditions for achieving finite-time synchronization and determining stability time under the influence of delayed impulsive effects were established. A comprehensive discussion on the interaction between impulsive effects and pinning strategies was also included. It was noted that integrating impulsive effects with pinning ratios enabled precise control over nodes exhibiting significant errors, thereby promoting rapid convergence within finite time frames. Our findings highlight the effectiveness of impulsive pinning control in enhancing synchronization stability, providing significant insights into the practical applications of complex-valued neural networks, particularly in image processing.
- finite-time synchronization (FTS),
- complex-valued neural networks (CVNNs),
- impulsive effect,
- pinning control ratio
Citation: Shuang Liu, Tianwei Xu, Qingyun Wang. Effect analysis of pinning and impulsive selection for finite-time synchronization of delayed complex-valued neural networks[J]. Electronic Research Archive, 2025, 33(3): 1792-1811. doi: 10.3934/era.2025081

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Abstract

We explored the phenomenon of finite-time synchronization for coupled complex-valued neural networks that were subject to mixed-variable delays. To address this challenge, an impulsive pinning control strategy was proposed. The method presented entailed the dynamic adjustment of specific nodes at distinct impulsive intervals, contingent upon the magnitude of the errors observed in those nodes. Furthermore, an enhanced technique utilizing the sign function was employed to simultaneously manage the real and imaginary components of the complex-valued neural networks. By applying finite-time stability theorems and utilizing complex-valued inequalities, sufficient conditions for achieving finite-time synchronization and determining stability time under the influence of delayed impulsive effects were established. A comprehensive discussion on the interaction between impulsive effects and pinning strategies was also included. It was noted that integrating impulsive effects with pinning ratios enabled precise control over nodes exhibiting significant errors, thereby promoting rapid convergence within finite time frames. Our findings highlight the effectiveness of impulsive pinning control in enhancing synchronization stability, providing significant insights into the practical applications of complex-valued neural networks, particularly in image processing.

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