Componentwise Stability of BAM Neural Networks with Uncertainties (original) (raw)

In this paper, without assuming the boundedness, monotonicity and differentiability of the activation functions, we present new conditions ensuring existence, uniqueness, and global asymptotical stability of the equilibrium point of bidirectional associative memory neural networks with fuzzy logic and time delays. The results are applicable to both symmetric and nonsymmetric interconnection matrices, and all continuous non-monotonic neuron activation functions. Since the criterion is independent of the delays and simplifies the calculation, it is easy to test the conditions of the criterion in practice. An example is given to demonstrate the feasibility of the criterion.I. Introduction Bidirectional associative memory (BAM) neural networks known as an extension of the unidirectional autoassociator of Hopfield [1] was first introduced by Kosto[2]. It is composed of neurons arranged in two layers. The neurons in one layer are fully interconnected to the neurons in the other layer, while there are no interconnection among neurons in the same layer. Through iterations of forward and backward propagation information flows between the two layers, which performs a two-way associative search for stored bipolar vector pairs and generalize the single-layer auto-associative Hebbian correlation to a two-layer pattern-matched heteroassociative circuits. Due to the BAM neural networks has been used in many fields such as pattern recognition, image processing, and automatic control. Therefore, the BAM neural networks have attracted great attention of many researchers .One can refer to the articles [3-18] for detailed discussion on these aspects. When a neural network is employed as an associative memory, the existence of many equilibrium points is a necessary feature. However, in applications to parallel computation and signal processing involving solution optimization problems, it is required that there be a well-defined computable solution for all possible initial states. From a mathematical viewpoint, this means that the network should have a unique equilibrium point that is globally asymptotically stable. In hardware implementation, time delays occur due to finite switching speeds of the amplifiers, and the existence of time delays frequently causes oscillation or instability in neural networks, Thus, the study of globally asymptotical stability of BAM neural networks with time delays is practically required. In [12-18], some sufficient conditions have been obtained for globally asymptotic stability of delayed bidirectional associative memory networks. In this paper, we investigate a kind of delayed BAM neural networks with fuzzy logic which integrates fuzzy logic into the structure of traditional BAM neural networks with time delays. Unlike traditional BAM neural networks structures, the kind of BAM neural networks has fuzzy logic between its template and input besides the operation of sum of product. Studies have been revealed that neural networks with fuzzy logic has inherent connections to mathematical morphology ,which is a cornerstone in image processing and pattern recognition[19]. Some results on stability have been derived for fuzzy neural networks, for example [20-22], but few studies have considered the stability for the BAM neural networks with fuzzy logic. Our objective is to study the existence of unique equilibrium point and its global asymptotic stability for delayed BAM neural networks with fuzzy logic. Without assuming the boundedness, monotonicity and differentiability of activation functions, by using M-matrix theory, Liapunov functions, we present new conditions ensuring existence, uniqueness, and global asymptotical stability of the equilibrium point for the class of BAM networks with fuzzy logic and time delays.