General Decay Stability of Theta Approximations for Stochastic Delay Hopfield Neural Networks

Kai Liu (), Guodong Qin, Linna Liu and Jumei Wei ()
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Kai Liu: School of Science, Henan University of Engineering, Zhengzhou 451191, China
Guodong Qin: School of Industrial Software, Henan University of Engineering, Zhengzhou 451191, China
Linna Liu: School of Electric and Information Engineering, Zhongyuan University of Technology, Zhengzhou 451191, China
Jumei Wei: School of Mathematics and Statistics, University of Zhengzhou, Zhengzhou 450001, China

Mathematics, 2025, vol. 13, issue 16, 1-15

Abstract: This paper investigates the general decay stability of the stochastic linear theta (SLT) method and the split-step theta (SST) method for stochastic delay Hopfield neural networks. The definition of general decay stability for numerical solutions is formulated. Sufficient conditions are derived to ensure the general decay stability of the SLT and SST methods, respectively. The key findings reveal that, under the derived sufficient conditions, both the SLT and SST methods can achieve general decay stability when θ ∈ 1 2 , 1 , while for the case of θ ∈ 0 , 1 2 , the stability can also be guaranteed, which requires a stronger constraint on the step size. Finally, numerical examples are provided to demonstrate the effectiveness and validity of the theoretical results.

Keywords: general decay stability; stochastic delay Hopfield neural networks; split-step theta method; stochastic linear theta method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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