Study And Application On Stochastic Models Of Spiking Neurons And Their Coupled Systems

With the development of physics, math, biology and computer, the investigation on brain has gained great achievements, especially the research on neural model. Scientists work on all kinds of neural models, trying to disclose the signal storing and processing of the brain, build brain model of cognition and realize the annual intelligence at last. Usually the scientific research begins from simple to complex, so the spiking neuron models and their coupled neural nets were selected as the main subject of this dissertation. Their nonlinear dynamic characteristics and signal transmission were studied. The role of noise was also discussed in the signal processing of the neuron models and net. The results show that noise is helpful to the signal processing through stochastic resonance. The characteristics of signal transmission were analyzed to reveal the neuron's signal processing mechanism. These results are a kind of explanation of neural biological and physiological experiments in the models, are of significance to the experiments and treatments of some neural diseases.The main contents and results of this thesis are as follows:1. The studies on spiking neuron and net in recent years were reviewed, especially stochastic resonance in neural models. The firing characteristics and nonlinear dynamics of Hodgkin-Huxley (HH) and FitzHugh-Nagumo (FN) spiking neuron models were investigated.2. The effects of high frequency (HF) signal on HH neuron stochastic model were studied. The HF signal inhibited the spiking of neuron, which was consistent with the physiological results. It was also similar with the two-tone suppression of auditory neuron. In addition, the HF signal could induce the resting potential change into high frequency oscillation. These results may be used to explain the corresponding physiological phenomenon.3. The transmission of suprathreshold signal and multi- frequencies signals in the stochastic HH neuron model was investigated. Their transmission was influenced by noise through suprathreshold stochastic resonance. The model was of frequency sensitivity, similar to bandpass. It was alike the characteristics of auditory system, so it could be used to discuss the frequency selectivity of auditory neuron. The noise could change the sensitive frequency, i.e., the shift of center frequency of bandpass. It is of significance to signal processing method.4. The transmission of subthreshold signal in FN stochastic model was investigated. The results showed that there was stochastic resonance and the transmission of sinusoidal signal was closely correlated with its frequency. The neuron model responded strongly with frequencies in the range of 0.2~0.8. Accordingly, the self firing activity of auditory neuron was analyzed. 5. The one-way coupled HH neuron system was simulated. The suitable noise would improve the efficiency of signal transmission. In addition, the noise and coupling coefficient of suitable intensity could make the system be in lag synchronization. The lag synchronization was redefined and analyzed according to the characteristics of stochastic system. In a one-way coupled system composed of 100 FN neurons, the lag synchronization was found, too. The self firing induced by strong coupling and the inhibition of firing induced by noise can be used to explain the corresponding phenomena of neuron.6. The frequency sensitivity of the one way coupled HH neural system was investigated for the first time. The activities of the receptor changed with the variation of the parameters, i.e., the sensitive frequency changed with the noise and coupling. The transmission of multi-frequency signals was consistent with single-frequency signals. The noise was bad to the frequency sensitivity. The one way coupled neural net was alike a bandpass device. In addition, the one-way coupled net origins from central pattern generator, so the results can be used to explain the generating mechanism of its rhythm.7. The effect of noise in the image processing of Pulse Coupled Neural Networks (PCNN) was simulated. It showed that noise could improve the results of image filtering and image enhancement. The PSNR and MSE of images also showed the existence of stochastic resonance. This study expands the fields of stochastic resonance, and is helpful to the study of image processing method.