Dynamical Analysis On Mixed Bursting In The Pre-B(?)tzinger Complex

Respiratory movement is a rhythmic activity that helps mammals to maintain individual life.It has rich dynamic behaviors.The pre-B(?)tzinger complex in ventrolateral medulla oblongata of human and other mammals contains a network of oscillatory bursting neurons,which is closely related to the generation of inspiratory phase of the respiratory rhythm.Theoretical and experimental results have suggested that respiratory system model can not only produces INaP-dependent somatic bursting and ICAN-dependent dendritic bursting,it also produces a somato-dendritic bursting depends on both currents.One special somato-dendritic bursting observed experimentally is that so called mixed bursting characterized by containing different types of bursts in one periodic cycle.We considered a single-compartment model of a pre-BotC neuron featuring both persistent sodium(NaP)and calcium-activated nonspecific cationic(CAN)currents.Based on fast-slow decomposition,phase plane analysis and bifurcation analysis,we study the generation mechanism of different patterns of mixed bursting.The paper is mainly divided into five parts.The first section is the introduction.The second section presents the basic biological knowledge.In the third section,we show that the system can exhibit multiple patterns of mixed bursting each of which contain two or more different types of short bursts in one cycle of periodic solution.We reveal the dynamical mechanisms underlying those mixed bursting,and further investigate how the sodium conductance and the potassium conductance affect the patterns of mixed bursting.In the fourth section,we consider the effect of some other ion channels on the firing pattern of system.The last section is the summary of this thesis.