Autapse-induced logical resonance in the FitzHugh–Nagumo neuron

Abstract

It was demonstrated that the chaos-driven FitzHugh–Nagumo (FHN) neuron can be considered as a logic system to implement the reliable logical operations through the mechanism of logical resonance. 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 AND & NAND logical operations based on the autaptic FHN neuron model with time-varying coupling intensity. The numerical results demonstrate that there are the optimal ranges of parameters (including autaptic time delay, amplitude, frequency and phase fluctuation of autaptic coupling intensity) at which the reliability of logical operations can be maximized. Namely, autapse-induced logical resonance can be realized in the autaptic FHN neuron model. More interestingly, multiple logical resonances can be obtained by regulating autaptic time delay, phase fluctuation of autaptic coupling intensity, as well as frequency ratio between and autaptic coupling intensity and external periodic driving force. Finally, an intuitive interpretation for autapse-induced logical resonance is given based on the motion of the particle in the potential landscape.