Pattern And Bifurcation Analysis Of Mixed Bursting In The Coupled Pre-B(?)tzinger Complex Neurons

Respiratory movement is an indispensable rhythmic activity for mammals to maintain their life.Respiratory rhythms,whose center of generation is located in the pre-B(?)tzinger complex,is uniform and orderly in normal state,but disordered and irregular in pathological state.Therefore,it is of great significance to study the dynamic mechanism and control of respiratory rhythm.In this thesis,based on a two-coupled model of pre-B(?)tzinger complex with calcium ion current.In-phase and anti-phase burst are learned separately.The methods are including the phase-plane analysis,bifurcation analysis,fast-slow decomposition and ISI(InterSpike Interval)bifurcation sequence.The thesis is divided into four parts.The biological background,the basic knowledge of nonlinear dynamics used in this thesis and the research background,the research status of bursting at home and abroad are introduced firstly.In the second part,we mainly studies the influence of the persistent sodium conductance(gNap)and the intracellular concentration of IP3([IP3])on the in-phase pattern of excitatory neurons in the two-coupled model of pre-B(?)tzinger complex,and reveals the generation and transition mechanisms of different types of mixed bursting from a dynamic perspective.Furthermore,we also elucidate the effects of parameters gNap and[IP3]on the number of somatic bursts and dendritic bursts in the mixed bursting solution.In the third part,we investigate the generation and transition mechanisms of anti-phase bursting.Mixed bursting is also produced when the calcium ion concentration[Ca]is a constant value.The pattern and transition mechanisms of anti-phase bursting in the model are also studied.Conclusion and discussion are given in the last part.Studies in this thesis have shown that gNap and[IP3]has an important influence on the rhythmic activities of the coupled neuron model in the pre-B(?)tzinger complex.Under the influence of periodic fluctuations of[Ca]and the change of parameter gNap,the mixed bursting patterns of the coupled neurons are transformed from one pattern to another,and more complex bursting occurs.Additionally,our results show that the oscillation of calcium is not a necessary condition for the generation of mixed bursting.The results in this thesis may help us to better understand the irregular bursting in pre-B(?)tzinger complex and other neuron models.The methods used in this thesis can be applied to the study of other neuronal systems with multiple time scales.