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Abstract: This paper discusses a class of discrete time recurrent neural networks with multivalued neurons (MVN), which have complex-valued weights and an activation function defined as a function of the argument of a weighted sum. Complementing state-of-the-art of such networks, our research focuses on the convergence analysis of the networks in synchronous update mode. Two related theorems are presented and simulation results are used to illustrate the theory. [Copyright &y& Elsevier]

A multilayer neural network based on multivalued neurons (MLMVN) is a neural network with a traditional feedforward architecture. At the same time, this network has a number of specific different features. Its backpropagation learning algorithm is derivative-free. The functionality of MLMVN is superior to that of the traditional feedforward neural networks and of a variety kernel-based networks. Its higher flexibility and faster adaptation to the target mapping enables to model complex problems using simpler networks. In this paper, the MLMVN is used to identify both type and parameters of the point spread function, whose precise identification is of crucial importance for the image deblurring. The simulation results show the high efficiency of the proposed approach. It is confirmed that the MLMVN is a powerful tool for solving classification problems, especially multiclass ones. [ABSTRACT FROM AUTHOR]