Pulse-type hardware chaotic neuron model and its bifurcation phenomena.

Abstract

A number of studies has recently been made on hardware for a biological neuron for application to information processing functions of neural networks. A model of a single neuron with chaotic dynamics (called "the chaotic neuron model" proposed by Aihara) has the following properties of biological neurons: graded responses, relative refractoriness, and spatio-temporal summation of inputs. The model exhibits not only periodic responses but also chaotic responses for periodic stimulation. It is suggested that, with the chaotic neuron model, new information processing structures can be realized in neural networks. Accordingly, a single-neuron model should be designed so as to have the properties of biological neurons. But a pulse-type hardware chaotic neuron model has not been found. We previously proposed a pulse-type hardware neuron model composed of a negative resistance circuit, resistors, and capacitors. We reported also that the pulse-type hardware neuron model exhibited continuous firing for a constant stimulus current. But chaotic features of the neuron model have not been investigated. In this paper, we show, firstly, that the pulse-type hardware neuron model has the features of the chaotic neuron model, and we show that it is useful for the pulse-type hardware chaotic neuron model. Next, we show that the pulse-type hardware chaotic neuron model has three chaotic regions in the bifurcation diagram to periodic pulse train stimulation, and we clarify the bifurcation route and the return map in each chaotic region.