Improved Condition for ISS of Stochastic Memristive Fuzzy Cohen–Grossberg BAM Neural Networks with Time-Varying Delays

Abstract The primary objective of this paper is to conduct a comprehensive investigation into the model of a memristive fuzzy Cohen–Grossberg bidirectional associative memory neural network (MFCGBAMNN) that integrates time-varying delays and stochastic disturbances. This study aims to introduce an innovative approach for addressing the input-to-state stability (ISS) property within this intricate framework. To enhance the understanding of ISS characteristics in these networks, we develop a Lyapunov–Krasovskii function that is instrumental in analyzing stability amidst time-varying delays and stochastic disturbances, serving as a cornerstone for deriving sufficient conditions for ISS. In distinguishing this work from existing studies, we establish a stability analytical framework grounded in the Lyapunov–Krasovskii function. By employing non-smooth analysis techniques and stochastic analysis theory, we derive novel sufficient conditions for ISS. This methodology is particularly relevant to the complexities introduced by stochastic disturbances in the dynamics of neural networks. Moreover, the incorporation of set-valued maps in our analysis provides a solid framework for addressing the uncertainties inherent in memristive systems, thereby enhancing the reliability of the stability conditions derived. To substantiate our theoretical findings, we present two numerical examples that effectively demonstrate the applicability and efficacy of the proposed conditions.