Study On The Phase Resetting In Neural Dynamic System Of A Population Of Neurons With Different Phases

In recent decade, based on abundant data of neural electrophysiology experiments, mechanics and mathematics are used in the research of neural system dynamics and some novel dynamical mechanism, which are related to brain activity such as attention and memory, are discovered. And such methods have been given increasingly importance in brain science.This dissertation is based on the phase resetting model of one population of neuronal oscillators with certain amplitude of limit cycles referred to P.A.Tass's monograph. These neuronal oscillators possess the same characters. In this paper, I considered that different neuronal oscillator in a population had different characters such as eigen frequency and was effected by different stimulation pattern. A novel stochastic nonlinear model was proposed in this dissertation. The model focused on the phase resetting dynamic system, of which there was two different phases in a population of neurons. At present, phase resetting dynamics in medicine and biology has still kept in stage of one-dimension phase space analysis. The dissertation considered neural activities in higher-dimension phase space, which extended researching actuality and possessed important sense in neural information processing. The number density's evolution in two-dimension phase space described the encoding process of neural system. The conclusion was that compared with phase resetting dynamical model in one-dimension phase space, more neural information would be contained in higher-dimension phase space. That means the latter can express richer details in neural information processing but the former will lose some useful information.This dissertation researched not only neural oscillator's spontaneous activity, but also neural encoding process with stimulation. The evolution process of neural oscillator population will be presented respectively, when neural system is affected by different stimulation intensity or pattern. At this time, evolution processing of average number density item mostly depends on three factors which are stimulation intensity, and stimulation pattern and coupled intensity of neural oscillators. In the last chapter, the model obtained in this dissertation was successfully used to propose a dynamical mechanism of attention and memory, which provided a meaningful attempt in the quantitative research of cognitive neural science.