The Relativity Between Spiking Rate Of The Integrate- And-fire Neuron And Periodic Inputs

In this study, we apply a mean-field theory to reduce many synaptic inputs in order to investigate spiking behavior of a leaky integrate-and-fire neuron without noise driven by the synaptic input and periodic stimulation firstly. Numerical simulations show that the burstinglike behavior of the spike train occurs only when the amplitude is large enough for low input frequency, which is modulated by the input frequency. We find that the stimulation can cause a delay in the response of the neuron to its injected current at high input frequencies. However, noise is inevitable in the neuron dynamics. Then, we study the impact of periodic stimulation in the leaky integrate-and-fire neuron that includes noise originating from synaptic input. Using the Fokker-Planck equation, we can calculate the expression of instantaneous neuronal firing rate. The result of mathematical analysis and numerical simulations is that the maximal instantaneous firing rate of the integrate-and-fire neuron will become big when the input amplitude is large. When the input frequency becomes lower, the maximal value of the instantaneous firing rate will become bigger.