| Artificial neural networks are a method of abstraction,simplification,and simulation of the neural networks in the human brain from an information processing perspective.They consist of a large number of interconnected network neurons that form a structural model of neurons similar to that of the human brain,and thus,they can indirectly reflect some of the underlying properties of the human brain.The Bidirectional Associative Memory(BAM)neural network model works in a relatively simple way,it is capable of large-scale data processing.Therefore,this model has been widely used in the data processing.Although scholars focus on the continuous BAM neural network model,it is necessary to study the discrete BAM neural network model for better programming and numerical simulation.At the same time,delay is unavoidable in signal transmission and conversion process.Therefore,the study of discrete BAM neural network model with time delay makes the simulation more realistic.Firstly,based on the general stability criterion of the phase space of discrete-time systems with unbounded delays,we propose low-order and high-order discrete-time BAM neural network models with leakage,discrete and distributed delays.We prove the existence and uniqueness of equilibrium solutions in both types of models and verify their general stability(including exponential stability,polynomial stability,and logarithmic stability)using the method of non-singular M-matrices.Secondly,we propose a discrete-time BAM neural network model with composite Brownian motion as a random term and prove that the equilibrium solution with a random term is equal to that without a random term by using the law of large numbers.Then,we show the global general stability of the equilibrium solution in the mean square sense by constructing Lyapunov functions and linear matrix inequality(LMI)methods.Finally,we validate the effectiveness of the theoretical results through numerical examples.These research findings have significant implications for further understanding and applying the discrete-time BAM neural network models. |
