The search for periodic unstable orbits in periodically driven spike trains

Recently, periodic unstable orbits have been searched for in neural activity, by comparing the number of encounters in the original data and in surrogate data. Here it is shown that in periodically driven spike trains, ‘high’ numbers of encounters can be found because of the correlation of the discharge with the time-varying stimulus, without any relation with the structure of the system generating the discharge. The basic reason for the failure of the usual method for surrogate data when applied to spike trains is discussed and a new method to obtain surrogate data, specific for the time series of intervals from periodically driven spike trains, is introduced.