Single neuron model with recurrent excitation: Response to slow periodic modulation

The influence of a recurrent excitatory connection on the response of three neuron models to slow periodic modulation is analyzed. The models are the graded response model and the threshold model with and without adaptation. Lissajous displays of the system's output (discharge rate) as a function of the instantaneous input value show hysteresis in all three models. Hence, the outputs are different depending on whether the input is increasing or decreasing. Recurrent excitation increases the width of the hysteresis with (i) the frequency of the periodic modulation, (ii) the transmission delay of the recurrent connection, and (iii) the connection strength.