Functional possibility of chaotic behaviors in a single chaotic neuron model for dynamical signal processing elements

Dynamical behaviors of a single chaotic neuron model are studied by means of numerical methods in the context of dynamical signal processing. As external signals, six kinds of temporal spiking inputs with the same mean rate but different correlations of spiking intervals are employed. A decay effect of internal state of the neuron and a relative refractoriness play important roles in leading to complex dynamics of outputs categorized in the three types; (i) 1 or 0 responses, (ii) weak complex dynamical responses, and (iii) highly developed complex dynamical responses. In the responses of the categories (ii) and (iii), it is found that, typically, speaking, time structures of interspike intervals of inputs are reflected on dynamical properties of outputs even though mean interspike intervals of outputs are almost equal to all the inputs. We find that, by embedding of outputs in two dimensional space, higher order statistical features of spiking intervals of inputs are extracted with amplification of feature difference between them. Our results show that (i) the single chaotic neuron can work as a dynamical sampling element for inputs with sensitive responses to input and with noise robustness, and (ii) it can extract dynamical structures of inputs, for instance a second or higher order statistical features included in spike trains