Fixed-time synchronization of time-delayed fuzzy memristor-based neural networks: A special exponential function method

Yan Chen; Ravie Chandren Muniyandi; Shahnorbanun Sahran; Zuowei Cai; Yan Chen; Ravie Chandren Muniyandi; Shahnorbanun Sahran; Zuowei Cai

doi:10.3934/era.2025156

Electronic Research Archive

2025, Volume 33, Issue 6: 3517-3542. doi: 10.3934/era.2025156

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Fixed-time synchronization of time-delayed fuzzy memristor-based neural networks: A special exponential function method

1.
Faculty of Information Science and Technology, Universiti Kebangsaan Malaysia, Bangi 43600, Malaysia
2.
College of Information Science and Technology, Hunan Women's University, Changsha 410002, China

Received: 19 March 2025 Revised: 08 May 2025 Accepted: 20 May 2025 Published: 09 June 2025

This research focuses on controlling fixed-time synchronization (FixTS) in a time-delayed fuzzy memristor-based neural network (TDFMNN). To achieve FixTS and improve convergence speed, a discontinuous state feedback controller (StFC) incorporating a unique exponential function is developed for the memristor-based neural network (MNN) drive-response system (DRS). The FixTS is analyzed using the indefinite derivative Lyapunov function approach. The proposed TDFMNN incorporates multiple factors, such as memristor, time-variation of coefficients, time-delay, and fuzzy elements, making the model more practical compared to existing studies. The StFC is designed using the fixed-time stability (FixS) theory of the exponential function, which requires few parameters, thereby simplifying controller design and implementation. Numerical simulations are conducted to evaluate the performance of the proposed control strategy on two-dimensional and three-dimensional TDMNNs.
- fixed-time synchronization,
- fuzzy memristor-based neural network,
- special exponential function method,
- state feedback controller,
- time-delay
Citation: Yan Chen, Ravie Chandren Muniyandi, Shahnorbanun Sahran, Zuowei Cai. Fixed-time synchronization of time-delayed fuzzy memristor-based neural networks: A special exponential function method[J]. Electronic Research Archive, 2025, 33(6): 3517-3542. doi: 10.3934/era.2025156

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Abstract

This research focuses on controlling fixed-time synchronization (FixTS) in a time-delayed fuzzy memristor-based neural network (TDFMNN). To achieve FixTS and improve convergence speed, a discontinuous state feedback controller (StFC) incorporating a unique exponential function is developed for the memristor-based neural network (MNN) drive-response system (DRS). The FixTS is analyzed using the indefinite derivative Lyapunov function approach. The proposed TDFMNN incorporates multiple factors, such as memristor, time-variation of coefficients, time-delay, and fuzzy elements, making the model more practical compared to existing studies. The StFC is designed using the fixed-time stability (FixS) theory of the exponential function, which requires few parameters, thereby simplifying controller design and implementation. Numerical simulations are conducted to evaluate the performance of the proposed control strategy on two-dimensional and three-dimensional TDMNNs.

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