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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]

The ability of bifurcating processing units and their networks to rapidly switch between different dynamic modes has been used in recent research efforts to model new computational properties of neural systems. In this spirit, we devise a bifurcating neuron based on control of chaos collapsing to a period-3 orbit in the dynamics of a quadratic logistic map (QLM). Proposed QLM3 neuron is constructed with the third iterate of QLM and uses an external input, which governs its dynamics. The input shifts the neuron''s dynamics from chaos to one of the stable fixed points. This way the inputs from certain ranges (clusters) are mapped to stable fixed points, while the rest of the inputs is mapped to chaotic or periodic output dynamics. It has been shown that QLM3 neuron is able to learn a specific mapping by adaptively adjusting its bifurcation parameter, the idea of which is based on the principles of parametric control of logistic maps [Proceedings of the International Symposium on Nonlinear Theory and its Applications (NOLTA''97), Honolulu, HI, 1997; Proceedings of SPIE, 2000]. Learning algorithm for the bifurcation parameter is proposed, which employs the error gradient descent method. [Copyright &y& Elsevier]