Dynamical Analysis Of FHN-ML Electrically Coupled Neurons

Along with the continuous development and progress of computational neuroscience,the firing patterns and bifurcation theory of various classical neuron models has been widely studied,such as Hodgkin Huxley model,Fitz Hugh Nagumo model and Morris-Lecar model and so on,these models lay the foundation for our in-depth analysis and discussion on the principle and operation mechanism of the nervous system‘s internal information coding.This article mainly based on the FitzHugh-Nagumo(FHN)and Morris-Lecar(ML)neuron model,through electrical coupling two Morris-Lecar neurons,as well as electrical coupling Fitz Hugh-Nagumo neuron with Morris-Lecar neuron,we can construct ML-ML model and FHN-ML model respectively.This article mainly studies the modified three-dimensional Morris-Lecar model,which increase a slow variable equation of electric on the basis of the original model,then make the neuron model to produce more abundant dynamic behavior.The main results are as follows:In the third chapter,we mainly study firing patterns and dynamics behavior of the ML-ML electrically coupled neuron model.Firstly,we regulated the value ofmembrane capacitance,ion channels time scale factors and other physiological parameters,and then study the effects on neuronal firing activities by numerical simulation.In accordance with the ISIs bifurcation diagram,we can further study the transformation between different kinds of firing patterns which contains typical nonlinear dynamic phenomenon,such as periodic bifurcation,inverse cycle bifurcation,period-doubling bifurcation,chaos,and various bifurcation phenomena mixed.Finally,we add the time-delay parameter in the equation,further consider the effects of time delay values on the firing patterns of the coupled neuron model.In the fourth chapter,we mainly study firing patterns and dynamics analysis of the FHNML electrically coupled neuron model.Firstly,we regulated the value of membrane capacitance,ion channels and related physiological parameters,and then study the effects on neuronal firing activities by numerical simulation.In accordance with the ISIs bifurcation diagram,we research the bifurcation process of the neuron more detailed.Secondly,based on the bursting discharge patterns,choose the slowly varying electric current of the ML neuron model as the bifurcation parameter,then use the fast-slow dynamic analysis to research the classification of the existing cluster.And then,add alternating current stimulation to the two neuron of the model respectively,discusses the effects of AC frequency and ion channel parameters values on the complex firing patterns of the neuron.Finally,increase the time-delay parameter to the equation on the basis of the original model,so that we can consider the influence of the time-delay values on the firing patterns and bifurcation of the model.