The Global Stability Of Some Bidirectional Associate Memory Neural Networks

The well-known bidirectional associate memory (BAM) neural networks wereinitially proposed by Kosko. These models generalized the single-layer autoassociativeHebbian correlator to a two-layer pattern-matched heteroassociative circuit. In the pastfew decades, this class of neural networks has attracted the attention of researchers. Thereason for that is their wide applications in associative memories, signal processing,pattern-recognition and neural control. Among various dynamical behaviors of BAMneural networks, global exponential stability is one of the most important andinteresting properties. Therefore, the investigation on the global exponential stability ofthe equilibrium has been the highlight in this field.In the first part of this article, the global exponential stability for continuous-timeand discrete-time BAM neural networks with delays is studied. A new method ofconstructing global Lyapunov functional for the continuous-time BAM neural networkwith delays is given by combining graph theory and Lyapunov method. Then asemi-discretization technique is proposed to approximate the continuous-time BAMneural network with delays. The results show that the discrete-time system has the sameequilibrium to its continuous-time counterpart, and can preserve global exponentialstability under the same principle. Moreover, a numerical example is provided to verifythe correctness of the conclusions.In the second part of this article, the global exponential stability for a stochasticBAM neural network with time-varying delays is studied. Some novel p th momentexponential stability principles are derived by combining inequality, graph theory,Lyapunov method, and stochastic analysis skills. These criteria have close relation withthe topology property of the BAM neural network. Finally, a numerical example isprovided to demonstrate the effectiveness and applicability of the theoretical results.