Investigation On The Dynamics Of The Neuron Model

Neuron system is of strong nonlinearity, as a extremely complicated and multi-layeredinformation network system composed by a large number of nerve cells which connect toeach other, complex nonlinear dynamics behavior would happen during the process of theneuronal electrostatic discharged and information coding. In this essay, exciting cells andunexciting cells discharge modes are took for the study objects. Numerical simulation anddynamic characteristic are performed and analyzed separately for each model, which hasestablished theoretical and practical sense.The main contents are as follows:Based on the model of HR、ML and Chay,we take additional considerations of outsideelectric field and electric current,a new nonlinear dynamic model is built.Using C languageprogramming for numerical calculation,and using Grapher software to draw map, we get thebifurcation map,phase and lyapunov inedx figure etc.Through the analysis of the originalmodel and new model’s in terspike in tervals bifurcation diagram, we get the dynamicbehavior of the system including the chaotic motion、periodic motion and so on.The analysisresults of specific models are as follows:(1)This essay studied the excited firing model under a single parameter bifurcationbehavior and bifurcation behavior under the two parameters, period-doubling bifurcation andperiod adding bifurcation are universal existence in the neuron discharge activity model.(2)By the contrast of single parameter bifurcation diagram and the parameters of thebifurcation diagram, fully shows that it’s necessary to discuss dynamics behavior of theneuron model under multiple parameter, has directive significance to the real-life.(3)Contrast two bifurcation maps that one is consider in trace electric field and the otheris not,verify the existence of external electric field interference with the function of thenervous system, analysis result neurons experiments provide a theoretical reference toneurons experiments.