A Unified Approach to Exponential Synchronization of BAM Neural Networks Involving Mixed Delays

Abstract

This paper investigates exponential synchronization for BAM neural networks incorporating delays in states, distributed delays, and arbitrary time scales. The neural model is rigorously analyzed to achieve exponential synchronization under different input conditions. Local stability criteria are first established based on necessary conditions. Theoretical proofs are then derived to characterize the stability phenomena and synchronization dynamics. The inclusion of two different delay terms, a state‐dependent delay term and an integral term with state dependent delay in the integrand and distributed delay in one of its limits that have not previously been discussed in the context of BAM networks on time scales constitutes the main novelty of this work. These terms improve the model's realism by capturing the intricate memory effects and transmission lags found in both artificial and organic neural networks. The unified time‐scale framework enables simultaneous handling of discrete and continuous systems, and thus the results are applicable to a broader class of dynamical systems. From an application standpoint, these delay structures are essential for simulating real‐world neural networks, where processing delays build up over a time‐varying window and signal transmission speed is dependent on the present state of neurons. The acquired exponential synchronization requirements offer helpful recommendations for the development of BAM network‐based systems for pattern recognition, associative memory, and secure communication. Finally, numerical examples are given to authenticate the obtained results and to emphasize the practical applicability.