Dynamics of the neural discharge in snail neurons

Spike trains recorded under weak sinusoidal driving from central neurons of Lymnaea stagnalis appear quite irregular and envisage the possibility of an underlying chaotic process. Therefore, the sequences of interspike intervals are analyzed in the framework of non-linear dynamics. Since, for several reasons, these sequences are rather short, the analysis is performed by using methods of non-linear forecasting. To reject the null hypothesis that the original time series is a realization of a linear stochastic process with the same autocorrelation function, the results obtained on the original data are compared with those from surrogate data sets. Some 'non-linear' predictability occurs only in narrow regions of the space of stimulus parameters and the frequency of perturbation is critical in determining it. Moreover, it is shown that such behavior can be qualitatively mimicked by the FitzHugh-Nagumo model driven by a weak sinusoidal signal plus noise. It is argued that the narrowness of the non-linear predictability regions renders quite unlikely the detection of deterministic dynamics in the activity of these neurons.