Asymptotical stability of fractional neutral-type delayed neural networks with reaction-diffusion terms

Wu, Xiang; Liu, Shutang; Wang, Yin; Liu, Zhibin

doi:10.1016/j.neucom.2021.07.042

Cited by 10 publications

(1 citation statement)

References 46 publications

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“…In recent years, fractional-order systems have become the focus of research, and articles [18][19][20][21] provide stability analysis of Riemann-Liouville neural networks. In the article, 22 the finite-time stability analysis of fractional-order amnestic fuzzy cell neural networks (MFFCNNs) with time delays and leakage terms was studied by using generalized Bernoulli's inequality and Holder's inequality.…”

Section: Introductionmentioning

confidence: 99%

Convergence analysis of Riemann‐Liouville fractional neural network

Dong

Liao

et al. 2022

Math Methods in App Sciences

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Many fractional order calculus researchers believe that fractional order calculus is a good way to solve information processing as well as certain physical system modeling problems. In the training of neural networks, there is the problem of long convergence time. In order to shorten the convergence time of the network, an R-L gradient descent method is proposed in this study. The article begins with a theoretical proof of the convergence of fractional order derivatives using function approximation and interpolation inequality theorems. Finally, through multiple simulations, it can be obtained that the fractional-order neural network can maintain a higher accuracy rate compared with the integer-order neural network, and also can well solve the problem of longer convergence time of the neural network. The convergence time can be reduced by nearly 10% compared to the integer order.

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Section: Introductionmentioning

confidence: 99%

Convergence analysis of Riemann‐Liouville fractional neural network

Dong

Liao

et al. 2022

Math Methods in App Sciences

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New fixed-time stability criterion and fixed-time synchronization of neural networks via non-chattering control

Tang

Wang

et al. 2022

Neural Comput & Applic

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Stability of Fractional Reaction-Diffusion Memristive Neural Networks Via Event-Based Hybrid Impulsive Controller

Wang,

Liu,

et al. 2024

Neural Process Lett

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This article explores the asymptotic stability of fractional delayed memristive neural networks with reaction-diffusion terms. A novel hybrid impulsive controller triggered by a specific event is proposed to stabilize the network, thereby replacing the conventional approach of modifying network parameters. The proposed controller is proven to prevent Zeno behavior. Sufficient conditions for the asymptotic stability of fractional delayed memristive neural networks with reaction-diffusion terms are established through Lyapunov direct method, inequality techniques, Green’s theorem and impulse analysis. Furthermore, the proposed controller is theoretically shown to be more resource-efficient than the conventional one, and our work extends existing research to make it more suitable for practical application such as pattern recognition, image processing and so on. Finally, an example is provided to illustrate the validity of the findings.

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Asymptotical stability of fractional neutral-type delayed neural networks with reaction-diffusion terms

Cited by 10 publications

References 46 publications

Convergence analysis of Riemann‐Liouville fractional neural network

Convergence analysis of Riemann‐Liouville fractional neural network

New fixed-time stability criterion and fixed-time synchronization of neural networks via non-chattering control

Stability of Fractional Reaction-Diffusion Memristive Neural Networks Via Event-Based Hybrid Impulsive Controller

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