Inhibitory autapses enhance coherence resonance of a neuronal network

Abstract

The counterintuitive phenomenon that inhibitory autapses enhance coherence resonance (CR) is investigated in a Hodgkin–Huxley neuronal network, which can be well interpreted by post-inhibitory rebound (PIR) spikes. Noise can induce CR in the network with excitatory coupling. After introducing inhibitory autapses, multiple CRs induced by noise appear at multiple time delays of inhibitory autapses. The degree of CRs can be enhanced by inhibitory autapses with time delays approximating to 10 ms or the sum of 10 ms and multiples of the firing period. For these time delays, each delayed inhibitory current pulse can induce a PIR spike, which is a signature of the stable focus near the Hopf bifurcation. The degree of CRs can be reduced by inhibitory autapses for time delays nearly equaling multiples of the firing period, because the inhibitory autaptic current pulses take effect near the spikes, resulting in the reduced irregularity of the spikes. More detailed dynamics of CR is investigated in planes composed of every two parameters out of the noise intensity, the autaptic strength, and the time delay. The counterintuitive phenomenon that inhibitory autapses can enhance the CR degree is in contrast to the conventional notion that inhibitory effects suppress the neuronal activities, which not only enriches the content of nonlinear dynamics, but also provides an approach to modulate CR or the firing regularity of neuronal networks.