Time-Delayed Inertial Bidirectional Associative Memory Neural Network: A Dynamical Exploration

This research aims to investigate the dynamical characteristics of second-order bi-directional associative neural networks (BAM), a domain where existing literature primarily focuses on first-order neural networks. The study's primary objective is to conduct a qualitative analysis of BAM neural networks by examining the influence of time-delays. The theoretical exploration involves stability conditions and Hopf-bifurcation analysis to unveil the impact of time-delays during neuronal transmission, specifically in terms of two-neuronal BAM models. By choosing time-delay as a bifurcation parameter, the study proposes necessary and sufficient conditions using the Routh-Hurwitz stability criterion and transversality conditions. Moreover, the paper presents illustrative examples that vividly demonstrate the effects of stability and Hopf bifurcation resulting from time-delays on the dynamics of neural networks. This research contributes to a deeper understanding of the intricate behaviors of second-order BAM neural networks in the context of time-delay dynamics.