Autapse-induced logical resonance in the FitzHugh–Nagumo neuron

It was demonstrated that the chaos-driven FitzHugh–Nagumo (FHN) neuron can be considered as a logic system to implement the reliable logic operation through logical resonance. Signal transmission between neurons is dependent on an essential component called synapse. Autapse (meaning the self-synapse) widely exists in various kinds of neurons, and it significantly affects the neuronal dynamics and functionalities. However, the effects of autapse on logical resonance have not been reported yet. Here, we explore the effects of autapse on the reliability of logical operation based on the autaptic FHN neuron with time-dependent coupling intensity. Our results demonstrate that there are the optimal ranges of autaptic time delay τ, the amplitude and frequency of coupling intensity, and phase fluctuation at which the reliability of logical operation can be maximized. That is, autapse-induced logical resonance can be realized in the autaptic FHN neuron. More interestingly, multiple logical resonance can be observed by regulating time delay, frequency ratio between oscillating coupling intensity and external input, and phase fluctuation. The results presented here provide the novel phenomena, and may have implications in understanding the logic gate-like functionalities in the nervous systems.