Evoking complex neuronal networks by stimulating a single neuron

Abstract

The responses of electrically coupled neuronal network to external stimulus injected on a single neuron are investigated. Stimulating the largest-degree neuron in the network, it is found that as the intensity of the stimulus increases, the network will be transiting from the resting to firing states and then restoring to the resting state, thereby showing a bounded firing region in the parameter space. Furthermore, it is found that as the coupling strength among the neurons decreases, the firing region is gradually expanded and, at the weak couplings, it could be separated into several disconnected subregions. By a simplified network model, we conduct a detailed analysis on the bifurcation diagram of the network dynamics in the two-dimensional parameter space spanned by stimulating intensity and coupling strength, and, by introducing a new coefficient named effective stimulus, explore the underlying mechanisms for the modified firing region. It is revealed that the coupling strength and stimulating intensity are equally important in evoking the network, but with different mechanisms. Specifically, the effective stimuli are shifted up globally by increasing the stimulating intensity, while are drawn closer by increasing the coupling strength. The dynamical responses of small-world and random complex networks to external stimulus are also investigated, which confirm the generality of the observed phenomena. The findings shed new lights on the collective behaviors of complex neuronal networks and might help our understandings on the recent experimental results.