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This article is concerned with the problem of the number and dynamical properties of equilibria for a class of connected recurrent networks with two switching subnetworks. In this network model, parameters serve as switches that allow two subnetworks to be turned ON or OFF among different dynamic states. The two subnetworks are described by a nonlinear coupled equation with a complicated relation among network parameters. Thus, the number and dynamical properties of equilibria have been very hard to investigate. By using Sturm’s theorem, together with the geometrical properties of the network equation, we give a complete analysis of equilibria, including the existence, number, and dynamical properties. Necessary and sufficient conditions for the existence and exact number of equilibria are established. Moreover, the dynamical property of each equilibrium point is discussed without prior assumption of their locations. Finally, simulation examples are given to illustrate the theoretical results in this article. [ABSTRACT FROM AUTHOR]

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]

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]

This paper proposes temporal-to-spatial dynamic mapping inspired by neural dynamics of the olfactory cortex. In our model the temporal structure of olfactory-bulb patterns is mapped to the spatial dynamics of the ensemble of cortical neurons. This mapping is based on the following biological mechanism: while anterior part of piriform cortex can be excited by the afferent input alone, the posterior areas require both afferent and association signals, which are temporally correlated in a specific way. One of the functional types of the neurons in our model corresponds to the cortical spatial dynamics and encodes odor components, and another represents temporal activity of association-fiber signals, which, we suggest, may be relevant to the encoding of odor concentrations. The temporal-to-spatial mapping and distributed representation of the model enable simultaneous rough cluster classification and fine recognition of patterns within a cluster as parts of the same dynamic process. The model is able to extract and segment the components of complex odor patterns which are spatiotemporal sequences of neural activity. [ABSTRACT FROM AUTHOR]