Responses Of Neuronal Systems On Complex Network To Stimuli

The response of neuronal networks to stimuli is an important issue in the study of the function and structure of brain. The communication between different areas in neural systems relies on the responses of local neuronal networks to the input signals. And the structure of networks impacts on the dynamics of networks. In this thesis, we study the responses of populations of neurons to stimuli on global-coupled and scale-free networks, address the relations of the encoding behaviors to the intensity of stimuli, the percent of excitatory synapses and the structure of networks.First, the responses of the global-coupled H-H neuronal networks to the spike-train input are studied. The global-coupled neuronal networks respond the periodical spike-train input by the collective oscillation. The activities of neuronal ensembles form the temporal-spatial patterns encoding the input stimuli. In the proper schemes of the system, the output of networks conserves the characteristics of input signals. A threshold of the percent of excitatory synapses exists, above which the non-stimulated neurons oscillate with the frequency locked to the input signals. As the intensity of stimuli increases, the threshold of the percent of excitatory synapses changes non-monotonically which first decreases and then increases. The enhancement of the intensity of stimuli reduces the difference between the ensembles of stimulated and non-stimulated neurons, and induces that the two ensembles of neurons respond with the same frequency.The relations between the inter-spike interval (ISI) of input and output signals show that the refractory of networks is larger than individual neurons. The minimum ISI allowed by the frequency-locked response decreases as the intensity of stimuli increase. While it first decreases and then increases as the percent of excitatory synapses increases.The average activity of the ensemble of non-stimulated neurons rises with the increase of the intensity of stimuli and the percent of excitatory synapses respectively, and saturates after a value of these parameters. The coherence measure of the ensemble of non-stimulated neurons changes non-monotonically with the percent of excitatory synapses, which first decreases and then increases. For the points of the minimum output ISI of the ensemble of non-stimuli neurons in frequency-locked oscillation, the average activity and the coherence measure, it is most advantageous to encoding and transmitting signals that the number of excitatory synapses matches the inhibitory synapses.Second, the responses of neuronal networks with scale-free property to stimuli were studied. The phenomena, i.e., the frequency-locked oscillation of neuronal ensembles and the threshold of percent of excitatory synapses etc, are similar with that of the global-coupled neuronal networks. The effects of network structure on the responses are follows:The threshold of average degree of networks exists in scale-free neuronal networks, above which the non-stimulated neurons oscillate with the frequency locked to the input signals. The threshold decreases as the percent of excitatory synapses increases. If all synapses are excitatory, in global-coupled networks the ensemble of non-stimulated neurons encode signals by firing in the exactly same timings, whereas in scale-free networks only partial non-stimulated neurons fire in the exactly same timings. The percents of excitatory synapses and intensity of stimuli for producing 1:1 frequency-locked oscillation in scale-free networks are larger than those of global-coupled networks. The increases of the intensity of stimuli, the percent of excitatory synapses and the average degree of networks enhance the average activity of the non-stimulated neuron ensembles. The average activity of scale-free networks can be higher or lower than that of global-coupled networks in different regions of the parameters.Additionally, the effects of average degree on the pattern recognitions of scale-free Hopfield networks are studied. It is found that if the ratio of the number stored in the model P to the size of the network N is less than 0.1, the following results exist. The overlap between the stable state of networks and the pattern is independent of the size of networks. And the relation between the overlap and the ratio of links of new nodes to the number of patterns abides by the sigmoidal curve.