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my guess from my very basic knowledge is that the bigger the stimulus the larger the influx of initial sodium ions into the neurone. therefore an action potential is triggered in the first segment of the neurone. the sodium ions move from the first segment to the second segment and due to the movement of sodium ions from the action potential and the movement of sodium ions from the initial stimulus this is enough to trigger a second action potential quickly.
a smaller stimulus must have a smaller influx of sodium ions initially so its harder for the sodium ions to spread out as much as there's not the same amount (same amount from action potential but not same amount due to the stimulus)
Voltage-gated Na+ channels are only transiently open and will very quickly inactivate after they are stimulated to open. The time taken for these channels to recover back into the closed state as well as the cell to repolarise is what is responsible for the refractory period of the nerve. During this time, only a large stimulus will be able to fire the nerve, whereas small stimuli are only able to fire the nerve when it has returned to resting potential. This is why large stimuli can cause higher frequency firing - there is shorter time before they can stimulate the nerve again.