| Neural biophysics is a subject to study the most complex system: nerve system including the brain, and it become one of the most pop field in 21 century. The goal of the research is to understand how neurons can exhibit animal behavior. Therefore, it need to understand the internal characteristic of single neuron, including how it form a signal, and how it response to external stimulus. In addition, neurons are not act alone, they connect to each other to form a network. The network can perform a certain function.As we know, nerve system works in a noisy environment. However, it can still apperceive, differentiate and deal with information effectively. Therefore, focus on the stochastic phenomena, this thesis organized according to the order from neuron to neural networks. The goal of this dissertation is to know how the nerve system can deal with information effectively at different levels under the control of noise and other parameters.In single cell level, the effects of temperature on the spontaneous action potential at finite patch size membrane are studied. Firstly, base on the determinate HH model, it is found that with the increasing of patch temperature, neurons are hard to be excited, and the amplitude of action potential is reduced. Then, based on the random opening and closing of ion channels, we consider the random HH model. By virtue of numerical and analytical method, we got the following results. With the increasing of patch temperature, it is found that (1) the mean open rate of sodium and potassium channels of the HH neuron are decreased, and the mean duration of spikes of membrane potential is also decreased, which are qualitatively consistent with previous experimental results of single ion channel. (2) Under moderate patch size, the mean inter-spike interval of membrane potential first decreases, reach a minimum, and then increases with the increasing of patch temperature. (3) By defining a measure parameterβ, we show that there is a maximal region for the measureβin the patch temperature and patch size parameter plane where the coherence resonance phenomena are very remarkable, and the characteristic time of the output also confirm our result.In the level of neuron ensemble, we studied the effect of coupling on the ability of neuron ensemble transmission the external signal precisely. It is found that the spatial correlations of neuron noise is better for improving synchronous firing of neurons and the spike timing precision. In addition, there is an optimal coupling length, corresponding to the biggest response state, i.e., local correlation of noise is advantage for signal transmission. In the presence of electrical synapse, the ability of the neuron ensemble transmitting the aperiodic signal precisely can be enhanced at certain optimal coupling strength for the case of moderate noise. However, it is decreased with increasing coupling strength in the case of small noise intensity. In the case of large noise intensity, although the spike timing precision and the power norm are increased with increasing coupling strength, yet it is interesting that there is a valley for both spike timing precision and power norm in certain range of the coupling strength. By using of membrane potential distributions, we give the possible mechanism of electrical coupling.Finally, a much complex but much close to the natural neuron system model is considered: feed-forward neural network. The influence of the connection probability between nearest layer and the ratio of the inhibition connections to the total connection are investigated. It is found that there is an threshold, beyond which the firing rate of each layers can propagate through the whole network. In company with the propagation of the firing rate, synchronization among neurons in the same layer is happened. When the inhibition connection is considered, it offset the excitation input and reduce the firing rate. In the case of balance excitable and inhibitable connections, the output rate is the most irregular.
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