Study On Mixed-mode Bursting In The Coupled Pre-b(?)tzinger Complex Neurons

Respiratory movement is an important physiological activity for all mammals,including humans,which rely on breathing exercises to support life.The Pre-B(?)tzinger complex is a key part of the origin of respiratory rhythm in newborn mammals,and it is the center of respiratory rhythm.In this paper,two coupling neurons in the Pre-B(?)tzinger complex are studied.We study the mixed-mode bursting and their transition mechanisms in two different dynamical models of these coupled neurons,respectively.This paper is divided into four parts:the first part is the introduction,includes the research background,the research status of bursting,and some theories of the neurons and the nonlinear dynamics,which is including the structure of neurons,the action potential and the fast-slow analysis,etc.In the second part,we mainly studies the generation and transition of the mixed-mode bursting in the coupled neurons,and the effect of potassium concentration on the mixed-mode bursting is studied by the method of fast-slow analysis.In the third part,using bifurcation analysis and two-parameter bifurcation analysis,we mainly study the effects of concentration of calcium ion on the mixed-mode bursting,which caused the change of relative position of saddle-node bifurcation and Hopf bifurcation.Conclusion and discussion is given in the last part.In this paper,there are two factors which related to the generation of mixed-mode bursting.Change of concentration of potassium ion leads to the generation of mixed-mode bursting.The fluctuation of concentration of calcium ion causes the change of relative position of bifurcation curves,including saddle-node bifurcation and Hopf bifurcation,which causes the generation of the mixed-mode bursting.the method used in this paper for studying the mixed-mode bursting can not only provide a new thought,also can be extended and applied to other rhythmic nervous system with fast-slow time scale.