Almost Sure Exponential Stability of Uncertain Stochastic Hopfield Neural Networks Based on Subadditive Measures

Zhifu Jia and Cunlin Li ()
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Zhifu Jia: School of Sciences and Arts, Suqian University, Suqian 223800, China
Cunlin Li: Ningxia Key Laboratory of Intelligent Information and Big Data Processing, Governance and Social Management Research Center of Northwest Ethnic Regions, North Minzu University, Yinchuan 750021, China

Mathematics, 2023, vol. 11, issue 14, 1-19

Abstract: For this paper, we consider the almost sure exponential stability of uncertain stochastic Hopfield neural networks based on subadditive measures. Firstly, we deduce two corollaries, using the Itô–Liu formula. Then, we introduce the concept of almost sure exponential stability for uncertain stochastic Hopfield neural networks. Next, we investigate the almost sure exponential stability of uncertain stochastic Hopfield neural networks, using the Lyapunov method, Liu inequality, the Liu lemma, and exponential martingale inequality. In addition, we prove two sufficient conditions for almost sure exponential stability. Furthermore, we consider stabilization with linear uncertain stochastic perturbation and present some exceptional examples. Finally, our paper provides our conclusion.

Keywords: Hopfield neural networks; chance theory; almost sure exponential stability; Lyapunov method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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