Influence of autapse on mode-locking structure of a Hodgkin-Huxley neuron under sinusoidal stimulus

We investigated the mode-locking behaviors of a Hodgkin-Huxley neuron with an autapse under sinusoidal stimulus. A neuron without an autapse can exhibit rich p:q mode-locking (i.e. p output action potentials generated by q cycles stimulations) behaviors with periodic stimuli. In the presence of the autaptic connection, the p:q mode-locking behaviors are completely reset. The autapse extends the scope of mode-locking. The autapse can enhance or suppress the status of mode-locking. Even for some specified autaptic parameters, the neuron could be driven into the sub-threshold oscillation. Our results suggested that the autapse can serve as a potential control option for adjusting the mode-locking firing behaviors. We also found that changing the delay time is much more effectively operable to regulate the response behavior than the autaptic intensity.