New Insights into Delay-Impulsive Interactions and Stability in Almost Periodic Cohen–Grossberg Neural Networks

This paper investigates the existence and global exponential stability of almost periodic solutions in a class of impulsive Cohen–Grossberg-type bidirectional associative memory (BAM) neural networks with time-varying delays. Real neural systems often experience sudden perturbations and nonuniform temporal interactions, leading to complex oscillatory behaviors. To capture these effects, a new impulsive Cohen–Grossberg BAM model is developed that integrates both delays and impulsive influences within a unified framework. Using the theory of almost periodic functions, fixed point methods, and impulsive differential inequalities, new sufficient conditions are derived for the existence and stability of almost periodic solutions. A Lyapunov functional combined with a generalized Gronwall-type inequality provides rigorous global exponential stability criteria. Numerical simulations confirm the theoretical analysis. The results extend existing studies and offer new insights into how delay and impulsive factors jointly shape the stability and dynamics of hybrid neural systems, contributing to the design of robust and delay-tolerant neural architectures.