Multi-Compartment Research And Dynamic Analysis Of Neuron Chay Model

Neuron is the structural basis and functional unit of the nervous system,which real-izes the transmission of neural information through multi-scale hierarchical connections.However,the single-compartment model of neuron is often difficult to fully character-ize its complex morphology and structure,so it is particularly important to study the characteristic of neuron by combining the two-or the multi-compartment research.In this paper,two types of compartmentalized neuron Chay models are established.We use bifurcation theory for dynamic analysis,and study abundant rhythms and patterns of firing through numerical simulation.The basic results are as follows:In Chapter 1,we briefly describe the important significance of neurodynamics in the research of the nervous system,the research status of neuron Chay model,and the main research contents of this thesis.In Chapter 2,we introduce the basic knowledge such as biological concepts and background,classical neuron models,bifurcation theory and research methods of neuro-dynamics.In Chapter 3,we analyze the dynamic bifurcation mechanism of the two-compartment neuron Chay model.First,the two-compartment neuron Chay model is established to explore the uniqueness and the dynamic change of the stability of the equilibrium point in the four-dimensional fast subsystem.Next,the slow variable is used as the bifurca-tion parameter,and the direction of the Hopf bifurcation is judged by the theoretical calculation of the first Lyapunov coefficient.Then,we study the biparameter bifurca-tion diagram of the system on the plane(gKV,VK),and obtain codimension 2 bifur-cation points such as Cusp bifurcation and generalized Hopf bifurcation.Furthermore,based on the fast-slow dynamics method,two kinds of bursting patterns are summa-rized as:the“fold/homoclinic”bursting via“fold/homoclinic”hysteresis loop and the“Hopf/homoclinic”bursting via“fold/homoclinic”hysteresis loop,while the transition mechanism is analyzed in detail.Finally,we study the influence of the inward-current correlation parameter VC and the out-current correlation parameter VK on the firing pat-tern and phase difference.The result shows that with the generation of period adding bifurcation,the neuron model can realize the transformation of the periodic solution of the system,and the realization of synchronization state is hindered by the slight difference of the inter-spike interval between the two compartments.In Chapter 4,we study the abundant rhythms and characteristics of firing of t-wo multi-compartment neuron Chay models.(1)The fifteen-compartment neuron Chay model is established.First,the effect of stimulation target on the representation of neural information is discussed.By comparing the first spike latency of 6 different stim-ulation target patterns such as single-compartment stimulation and two-compartment stimulation,the response law of neuron model to the change of stimulation target is re-vealed.Then,the influence of numerical simulation of demyelination on the rhythm and characteristic of firing is analyzed theoretically.(2)The one hundred and thirty-one-compartment neuron Chay model is established.First,the adjustment effect of dynamic changes of external stimulation Istim and maximum conductance gKV on the characteris-tic of firing activity is compared and analyzed through three kinds of information coding indexes.Then,three cases of missing structure are obtained by removing part of the central process structure,and compared with the normal morphological structure to s-tudy the differences in the effects on the rhythm and characteristic of firing of the neuron model.