Stability and synchronization of higher-order memristive Cohen-Grossberg bidirectional associative memory neural networks

This work investigates the stability and synchronization of higher-order memristive Cohen–Grossberg bidirectional associative memory neural networks. Due to the discontinuities generated by memristive effects, the analysis is carried out within the Filippov framework. By constructing appropriate Lyapunov functionals and applying refined analytical techniques, we derive general conditions that guarantee global stability with both exponential and polynomial convergence for a broad class of kernel functions extending existing models. Unlike many previous studies, the boundedness assumption on activation functions is removed, which prevents reduction to a linear system and introduces additional nonlinear complexities. These challenges are addressed using nonlinear analysis methods combined with a differential inequality approach. Moreover, synchronization between drive and response systems is achieved through adaptive feedback controllers with newly designed update laws. Numerical simulations are provided to validate the theoretical results. Let us start with new definition