Effects of hybrid synapses and partial time delay on stochastic resonance in a small-world neuronal network

In real neuronal systems, information transition delay is an inevitable factor. However, between some neurons, neuronal information is transmitted instantaneously or the time delay is too small and can be neglected. Thus, differing from the conventional studies where all connections are considered to be delayed, here we mainly focus on the effect of partial time delay on stochastic resonance in a Watts-Strogatz small-world neuronal network. Meanwhile, in the same neuronal network, the electrical and chemical synapses usually coexist. Thus, effects of hybrid synapses are also considered. Firstly, in the absence of time delay, noise could induce stochastic resonance when the neuronal network contains much more excitatory synapses than inhibitory ones; while it cannot induce stochastic resonance vise verse. Interestingly, it is further revealed that when the ratio of excitatory synapse to inhibitory synapse is approximately 4:1, noise-induced stochastic resonance is more robust. Thus, to discuss the effects of other factors on noise-induced stochastic resonance, we set this ratio to be 4:1. In the absence of time delay, we also consider effects of chemical synapses with a ratio of excitatory synapse to inhibitory synapse of 4:1 on the noise-induced stochastic resonance. The obtained results show that the noise could always induce stochastic resonance no matter how the probability of chemical synapses varies. And the optimal noise intensity increases linearly with the probability of chemical synapses increasing. For partial time delay, it is surprisingly found that the stochastic resonance could appear multiple times with the variation of the time delay being just for small partial time delay probability. Moreover, chemical synapse is found to facilitate this effect of partial time delay. Finally, by analyzing the joint effects of partial time delay and noise intensity, it is found that the larger the time delay and the partial time delay probability are, the wider the optimal noise region corresponding to large response amplitude is.