Phase-noise-induced resonance in a single neuronal system

Phase-disorder-induced resonance has been recently uncovered in an ensemble of coupled excitable neurons with weak external signal, where each neuron takes a constant initial signal phase. However, it is unclear how the initial phase disorder influences the behavior of a single or isolated neuron, which constitutes the ensemble. In order to answer this question, we here consider the case of a single neuron with phase noise originated from the time-varying initial signal phase, in contrast to the constant initial phase in each neuron studied in the above referenced paper. Interestingly, we find that the phase noise can induce resonance even in the single neuronal system with subthreshold signal. Moreover, we reveal that, with the presence of phase noise, the neuron also shows another resonance behavior by varying the period of the external signal. An analysis is conducted to uncover the mechanisms behind these resonance phenomena.