两类神经兴奋模型的递归图研究及应用概率论与数理统计专业论文.docxVIP

AbstractNeuroscience Abstract Neuroscience has always been a subject that people full of interest and willing to explore，it is a science to explain the biology mechanism of the intelligence activities．One of the important models in computational neuroscience is the Hodgkin—Huxley model of the squid giant axon．The model describes the pattern how the action potential generate and spread in neurons，and describes the electrophysiological properties of excitable ceils approx— imatively．Izhikevich model is another important one，the model is not only computationally simple，but can produce a variety of common types of cerebral cortex neurons，and is biologically plausible as the Hodgkin—Huxley model，yet as computationally efficient the integrate—and—fire model．Recurrence is fundamental concept in the theory of dynamical systems which refers to the system in the closed phase space will return to state that is very close to the initial state after sufficiently long time，Recurrence plot is a tool that make the recurrence visualized． This paper researchs Hodgkin—Huxley model，Izhikevich model and a list of the experi- mental measured spiking data using recurrence plot analysis．In the introduction，introducing the research history,,research status，research significance and research methods of dynam- ical systems in neuroscience．In the part of preliminary knowledge，introducing the basic concepts of recurrence plot and bifurcation．The main researchs in the paper include：1，US— ing recurrence plot analysis to study the bifurcation phenomenon of Hodgkin-Huxley model varying with parameter，and finding the bifurcation point；2，using recurrence plot analysis to study Izhikevich model，analyzing the characteristics of the recurrence plots，and distin— guishing different firing patterns of excitement；3，using plot analysis to analyze the experimental measured data of local field potentials the mouse’S visual neuron，and distinguishing firing patterns of experiment object according to the feature