Study Of Bursting Transitions Of In The Coupled Pre-B(?)tzinger Complex Neurons

Respiratory motion is an important aspect for mammal to maintain individual life. It has rich dynamic behavior of rhythmic activity. The generation center of respiratory rhythm is located in the mammalian ventrolateral medulla of pre-B(?)tzinger complex. There is a class of inspiratory neurons which closely related to the generation of respiratory rhythm and rhythmic bursting in the pre-B(?)tzinger complex.Based on the excitability of neurons, this paper focuses on the coupled pre-B(?)tzinger complex neurons. We study the bursting transitions and synchronization mechanisms in the Butera neuron model. The paper includes five parts. In Section Ⅰ, we give the research background of the respiratory system. In Section Ⅱ, we introduce the basic knowledge related to the nonlinear dynamics used in this paper. In Section Ⅲ, we study the dynamics of in-phase and anti-phase bursting in the coupled pre-B(?)tzinger complex. We use the fast-slow analysis, two parameter bifurcation analysis and phase difference method to study the transition mechanism and synchronization of the in-phase and anti-phase bursting in the coupled neuron, and we analyze the phase difference of the anti-phase bursting. In Section IV, we investigate the anti-phase bursting and synchronization in coupled pre-B(?)tzinger complex by phase difference method. We give the mechanism of bursting synchronization of coupled neurons. The conclusion is in the last section.The bursting transition and synchronization of neurons in the coupled pre-B(?)tzinger complex is an important aspect in the study of respiratory rhythm. The research shows that, the synchronization and transition of bursting has a close relationship. In this paper, two parameter bifurcation analysis and fast-slow analysis play a key role in the studies. The phase difference for spiking synchronization in the coupled neurons also plays an important role.In this paper, by means of the combination of nonlinear dynamics and numerical analysis, we study the effects of sodium conductance on the dynamic behavior of neurons in the coupled pre-B(?)tzinger complex. We provide some insights for further exploring the transition mechanism of respiratory rhythms.