Noise-Induced Simultaneous Firing in Uncoupled Leaky Integrate-And-Fire Circuits

In this paper, we report how uncoupled leaky integrate-and-fire oscillators exhibit simultaneous firing when common noise is applied. Specifically, we examined the probability of simultaneous firing resulting from circuit parameter mismatches caused by differences in the free-running periods of the oscillators. Focusing on the relationship between the trigger pulses generated from the applied noise and the firing events, we divided the oscillation period into individual characteristic time intervals under the assumption that the trigger pulses occur with uniform probability. Based on this approach, we derived a formula that relates the circuit parameter mismatches to the probability of simultaneous firing. The validity of this formula was confirmed through numerical simulations and was found to explain the experimental results effectively. The obtained results are useful in clarifying the probabilistic and statistical properties of the noise that result in the desirable trigger pulses.