Dynamic Preservation for a Class of Semi-Discrete Recurrent Neural Networks

Songfang Jia,Yanheng Chen

doi:10.1109/access.2021.3080981

Abstract

The dynamic preservation in discrete simulations of the recurrent neural networks (RNNs) with discrete and infinite distributive asynchronous time delays is addressed. Firstly, we formulate the corresponding discrete-time model by semi-discrete technique. Secondly, we derive several mild algebra conditions to guarantee that the discussed discrete-time system is the global exponential stability in Lyapunov sense. It is shown analytically that the discrete-time technique is able to maintain the uniqueness of equilibrium point and its dynamic behavior of the continuous-time model under the same conditions. Meanwhile, we also show that there exists some degree of deviation in the spatial position among the equilibrium points of the continuous-time model and its discrete-time analogue due to the rounding error. Finally, we verify the validity of the main obtained results by comparing one continuous-time numerical example with its discrete-time counterpart.

Highlights

As we all know, recurrent neural networks (RNNs) is a fundamental dynamic system, which is widely applied in the fields of optimal control, pattern recognition, prediction, and associative memory
We show some degree of deviation in the spatial position among the equilibrium points of continuoustime model and its discrete-time analogue due to the rounding error
The paper gets a discrete analogue for a class of RNNs with discrete and infinite distributive asynchronous delays by semi-discrete technique, and investigate its preservation of dynamic characteristics

Summary

INTRODUCTION

RNN is a fundamental dynamic system, which is widely applied in the fields of optimal control, pattern recognition, prediction, and associative memory. Zhou et al investigated the stability and periodicity for cellular neural networks with mixed asynchronous delays [10]. It is vital to find a suitable discrete method to preserve the dynamical behaviors of the continuous-time networks. Many scholars investigated the dynamic preservation in discrete simulations of continuous-time networks by semi-discrete technique [29]–[41]. Chen: Dynamic Preservation for Class of Semi-Discrete RNNs that the discrete analogues keep the periodicity of a class of integro-differential equations. The paper [38] illustrated the multi-almost periodicity of a semi-discrete neural network. According to the previous studies, there is no literature on the stability preservation of the semi-discrete RNNs with discrete and infinite distributive asynchronous time delays. We illustrate that the discrete model completely remain the dynamics of the corresponding continuous one.

PRELIMINARIES

MAIN RESULTS Theorem 1

DISCUSSIONS

CONCLUSION