Research On Phase Resetting In Neuronal Dynamical System

In the past one hundred years, especially middle to late the twentieth century, the great progress has been made in the neuroscience, so that many cross-subjects, which study the neuroscience in the microcosmic level, macro-level and mesoscope, are derived from neurobiology. One important filed of these subjects is that researching the neural dynamics and discovering the dynamics mechanics, which are related to brain activity just as memory and attention, by the mechanics and mathematics.Based on the phase resetting model of one neuronal oscillators population with certain amplitude, the thesis proposed a new stochastic nonlinear model. The model describes the phase resetting dynamics of the neuronal population with random amplitudes. After numerical analysis, we obtained the average number density's evolution, namely the neural coding, in the three-dimensioned space. Reconsidering that the different parts of the population are subjected to different stimulus or have different amplitude limit circles and dominant frequencies, we proposed the other model to describe the dynamics of the neuronal oscillators population.In this thesis, the author obtained some significant conclusions from theoretical analysis and numerical analysis, as follows:1.the conclusion proved that the Tass' suppose, which is that the limit circle of the amplitude equals one when the population with certain amplitude, was reasonable. But some neural coding was lost in this case, especially at the beginning of the evolution. The noise impacts on the width of the average number density's distributing on the amplitude, but the modality of the distribution is not changed if the noise intensity is notstrong enough. The initial condition and the coupling structure modality dominate the coding result. The higher order harmonic terms have not impact on the coding result, so that some information was filtrated when the neurons deal with the input.2. The stimulus plays an important role in the transformation of synaptic plasticity. The coupling structure and density within the neurons would be transformed after a long-timed stimulus, namely, that the synapse has been changed. The short-timed stimulus only transforms the coupling structure for a while. The coupling structure would resume the older through a process of resynchronization. It explained well the dynamics of memory and oblivion.3. The most neurons dominate the neural population's dynamics. It explains some mechanism of the attention. We would ignore the petit noise and image if we were absorbed in the main noise and image, for the reason that those neurons, subjected to the main noise and image, dominate the system activity when the brain processes the noise and images.The models and method in the thesis not only enriched the theory of phase resetting but also solved some problems of phase resetting in neural system dynamics. And the numerical analysis gave some evidences of theory and numerical value for researching the phase resetting of neural system dynamics, therefore, the thesis has important significance in theory and practice.