New stability results for bidirectional associative memory neural networks model involving generalized piecewise constant delay

Bidirectional associative memories (BAMs) have been extensively applied in autoassociative and heteroassociative learning. However, the research on the implementation of BAM neural networks model with the effects of the constant delay is relatively few. The present work accumulates the global exponential stability criteria for the BAM neural networks model with deviation arguments. Here the effects of the constant delay of generalized type are provided, namely piecewise constant delay of generalized type (in short, DEGPCD). This article is principally concerned with the existence and global exponential stability of the BAM neural networks model with the DEGPCD system by using approach based on the construction of an equivalent integral equation. Applying the linearization method, Banach's fixed point theorem, a DEGPCD integral inequality of Gronwall type and some inequality techniques, we establish a new sufficient condition to ensure the existence and global exponential stability of the equilibrium point of the BAM neural networks model with the DEGPCD system. The research indicates that the generalized piecewise constant delay has a vital effect on global exponential stability of the BAM neural networks model with the DEGPCD system. At the end of this work, the hypothesis has been established with two illustrative examples along with the simulations. (c) 2021 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.

Automated summary

This study presents global exponential stability criteria for the BAM neural networks model with constant delay effects and investigates the existence and stability of the model in the DEGPCD system using an equivalent integral equation approach. The research highlights the significant impact of generalized piecewise constant delay on the stability of the model.