It's my understanding that in ARP absolutely no action potential can be initiated, as all the Na channels are closed. In the ERP, a small fraction of channels are open, so that a large enough stimulus can cause an action potential. However, this fraction of available Na channels is so small that the elicited potential cannot be conducted to surrounding tissue. It remains locally, or to be more specific, it is an electrotonic potential.
10 years late to the thread, but here's a peer reviewed source about this topic:
Absolute refractory period (ARP): the cell is completely unexcitable to a new stimulus.
Effective refractory period (ERP): ARP + short segment of phase 3 during which a stimulus may cause the cell to depolarize minimally but will not result in a propagated action potential (i.e. neighbouring cells will not depolarize).
Relative refractory period (RRP): a greater than normal stimulus will depolarize the cell and cause an action potential.
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