Dynamics of continuous-time recurrent neural networks with random connection weights and unbounded distributed delays

Meiyu Sui; Yejuan Wang; Peter E. Kloeden; Xiaoying Han

doi:10.1140/epjp/s13360-021-01744-x

2022 Impact factor 3.4

EPJ PLUS - Condensed Matter and Complex Systems

Focus Point on Uncertainty Quantification of Modelling and Simulation in Physics and Related Areas: From Theoretical to Computational Techniques

Eur. Phys. J. Plus (2021) 136: 811
https://doi.org/10.1140/epjp/s13360-021-01744-x

Regular Article

Dynamics of continuous-time recurrent neural networks with random connection weights and unbounded distributed delays

Meiyu Sui¹^,2, Yejuan Wang¹, Peter E. Kloeden³ and Xiaoying Han⁴^d

¹ Gansu Key Laboratory of Applied Mathematics and Complex Systems, School of Mathematics and Statistics, Lanzhou University, 730000, Lanzhou, People’s Republic of China
² Hebei Key Laboratory of Computational Mathematics and Applications, School of Mathematical Sciences, Hebei Normal University, 050018, Shijiazhuang, Hebei, People’s Republic of China
³ Mathematisches Institut, Universität Tübingen, 72076, Tübingen, Germany
⁴ Department of Mathematics and Statistics, Auburn University, 221 Parker Hall, 36849, Auburn, AL, USA

^d xzh0003@auburn.edu

Received: 8 April 2021
Accepted: 8 July 2021
Published online: 6 August 2021

Abstract

A lattice system of continuous-time recurrent neural networks with random weights of connections among neurons and unbounded distributed time delays is studied. First the lattice system is formulated as a random nonautonomous functional differential equation on an appropriate functional space. Then the existence and uniqueness of solutions to the resulting functional differential equation are proved, and the longtime behavior in terms of existence of a pullback random attractor is investigated. In addition, extremal -complete quasi-trajectories for the cocycle generated by the functional differential equation are shown to exist by establishing a comparison theorem.