Control of sampling rate in map-based models of spiking neurons

The discrete-time (map-based) approach to modeling nonlinear dynamics of spiking activity in neurons enables highly efficient numerical simulations for capturing realistic neurobiological behavior by utilizing a large time interval between computed states (samples) of neuron activity. The design and parameter tuning of these models assumes a fixed and preset sampling rate. When change of the time step is needed, it requires revisiting stages of the model design and parameter tuning. This paper presents an approach to the design of map-models in a new form where time step is added as a control parameter and can be easily changed to vary the time scale of the model behavior, i.e. sampling rate, essentially preserving the model behavior. It also discusses modification of the noise generator models needed to support simulation of map-based neurons with the modified sampling rate. The effects caused by direct control of time scale on model dynamics and limitations of this approach are discussed.