Existence and periodic stability analysis of BAM neural networks under a generalized piecewise constant delay framework

Bidirectional associative memories (BAM) have found widespread applications in autoassociative and heteroassociative learning. Although BAM neural networks with various classes of delays have been extensively investigated, studies concerning generalized piecewise constant delay (DEGPCD) remain relatively limited. This paper focuses on the global exponential stability and periodicity of the BAM neural network model with deviation arguments, specifically the effects of generalized piecewise constant delay. We employ an approach based on the construction of an equivalent integral equation to establish the existence and global exponential stability of the unique 𝜔 -periodic solution of the BAM neural network model with the DEGPCD system. The linearization method, Banach’s fixed point theorem, a DEGPCD integral inequality of Gronwall type, and inequality techniques are used to establish a new sufficient condition for the existence and global exponential stability of the unique 𝜔 -periodic solution. Our research indicates that the generalized piecewise constant delay has a significant effect on the global exponential stability of the BAM neural network model with the DEGPCD system. Two illustrative examples with simulations are presented to validate the results.