Threshold fluctuation, the random firing of nerve cells exposed to a near-threshold stimulus, has been studied for many years both experimentally and theoretically. In a previous work of Lecar and Nossal, a reduced phase space approximation is used to reveal the origination of noise, which might be the random fluctuation of the membrane potential and the sodium conductance, according to their deduction.

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In this work, we confirmed their deductions both by plotting simplified functions and adding langevin force directly and doing iterative simulations to reproduce the results from a numerical view. We also take a trial on introducing full HH model into coding, and proposed possible plans to explore noise term under the condition of full HH model.