RESPONSE PROPERTIES OF A SINGLE CHAOTIC NEURON TO STOCHASTIC INPUTS

Abstract

Response properties of a single chaotic neuron to stochastic inputs are investigated by means of numerical simulations in the context of a nonlinear dynamical approach to analyzing chaotic behaviors of a neuron. We apply six kinds of stochastic inputs with the same mean rate but different correlations of interspike intervals, whose timings are determined by a stochastic process, namely, Markovian processes and Gaussian/Poisson random processes. From 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 calculations of Lyapunov exponents, trajectories of dynamics and return plots of internal states make meaningful difference in dynamical properties of the model depending on inputs even if mean interspike intervals of outputs are almost 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 space, 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 inputs. As conclusion, our results show that dynamical properties of inputs can be extracted with clear difference of response properties of the model, that is, the model gives a variety of the amplitude and the interspike intervals of outputs depending on inputs. In other words, the model can realize dynamical sampling of inputs with sensitivity of response properties to inputs and robustness to inputs with noise.