Slow dynamics of neuronal excitability under pulse stimulation

Neurons fire irregularly on multiple timescales when stimulated with a periodic pulse train. This raises two questions: Does this irregularity imply significant intrinsic stochasticity? Can existing neuron models be readily extended to describe behavior at long timescales? We show here that for commonly studied neuronal models, dynamics is not chaotic and can only produce stable and periodic firing patterns. This is done by transforming the neuron model to an analytically tractable piecewise linear discrete map. Thus we answer "yes" and "no" to the above questions, respectively.