Response properties of a single chaotic neutron to stochastic inputs

Response properties of a single chaotic neuron to stochastic inputs are inv estigated by means of numerical simulations in the context of a nonlinear d ynamical approach to analyzing chaotic behaviors of a neuron. We apply six kinds of stochastic inputs with the same mean rate but different correlatio ns of interspike intervals, whose timings are determined by a stochastic pr ocess, namely, Markovian processes and Gaussian/Poisson random processes. F rom numerical evaluations of entropy and conditional entropies with respect to interspike intervals of outputs, it is shown that interspike intervals of outputs represent dynamical structures of each input. Numerical calculat ions of Lyapunov exponents, trajectories of dynamics and return plots of in ternal states make meaningful difference in dynamical properties of the mod el depending on inputs even if mean interspike intervals of outputs are alm ost the same values. In order to extract dynamical features of outputs, we calculate a time-delayed space representation of output responses to inputs , and the results provide different trajectories in a time-delayed phase sp ace, which reflect a higher order statistical feature of inputs, amplifying their feature differences. For signals containing noise, the behaviors of the model do not suffer degradation, showing robustness to noise in the inp uts. As conclusion, our results show that dynamical properties of inputs ca n be extracted with clear difference of response properties of the model, t hat is, the model gives a variety of the amplitude and the interspike inter vals of outputs depending on inputs. In other words, the model can realize dynamical sampling of inputs with sensitivity of response properties to inp uts and robustness to inputs with noise.