Spiking Sychronization And Coherent Resonance Regulated By Noise In The Small-world Hodgkin-Huxley Neuronal Network

Nowadays, brain science, computer science and technology, information science and technology have been extensively developed. Brain science and computer science not only have their own unique characteristics, but also have some similar aspects in the processing of information and data. So combining brain science and computer information science to research has got more and more attention of the scientists.In the1950s, Hodgkin and Huxley through experiments and first proposed the-HH model for the description of discharge principle of single neurons. But the real human brain’s neural network system is composed by all the hundreds of millions of neurons, and each neuron interlinks the others. Complex network as the most popular network, it has been widely applied to the Internet, life sciences, sociology, physics and other disciplines. To research human brain network, the first thing is to construct a similar neuronal network connected by the same topology of the real brain network. At present, the study of biological neural networks shows that the small world network model and the real human brain neuron network model have the closest characteristics. So this paper introduces NW and WS small world network models from complex network, construct small-world neural network On the basis of the Hodgkin-Huxley model, and then study how the ion channel noise affects the neural network coherent resonance and spiking synchronization under different neuron cell membrane area, network connection probability p and synaptic conductance g.The conclusions obtained in this article are mainly the following two aspects:(1)The effects of internal noise on the coherent resonance of the small world neural networks. At this point, we consider the small-world networks with different connection probabilities. The results show that:with the increase of network connection probability, coherent resonance of the network increases monotonically; at the same time, the study also found that the effect of connection probability on stochastic resonance is the same as above.(2)The effect of external noise on the spiking synchronization of the small-world neural network:firstly, we found that the effect of external noise on the small-world neural network synchronization has two aspects. Noise can enhance the spiking synchronization for causing mutual spiking, on the other hand noise will reduce the synchronization for causing stochastic spiking. Due to the interaction of these two mechanisms, so there is the optimal noise intensity to produces the best synchronization; Secondly, if the coupling strength between neurons is too large or too small, then the noise-induced maximal synchronization disappears.Only when the coupling strength is the middle value, there is an optimal noise intensity to induce the maximal synchronization. Finally, if the noise intensity and coupling strength take a fixed value, the greater of the small world neural network connection probability, the maximal the spiking synchronization.