Multi-time Scale Analysis Of Mixed Bursting Within The Respiratory System

Respiratory movement is a basic activity of mammals for life maintenance.The pre-B(?)tzinger complex is the key neuronal kernel for the respiratory rhythm generation,and is locates at a subregion in the ventrolateral medulla of humans and other mammals.Neural firing rhythm is a way for encoding the information in the nervous system.In this paper,based on the excitatory neuron model in the pre-B(?)tzinger complex,the mixed bursting and their dynamic mechenisms are studied in the single as well as coupled pre-B(?)tzinger complex nourons under the influence of calcium dynamics.This paper is organized as follows:In Section 1,we present the bacground and basic knowledge about neuroscience and the dynamic theories related with our subject.In Section 2,we study the generation and transition mechenisms of mixed bursting in the single pre-B(?)tzinger neuron.Based on the multiple time scales theory,the effects of IP3 concentration on the mixed bursting are studied by means of fast-slow decompositon and bifurcation analysis.In Section 3,we study the influence of sodium conductance(gNa)on the mixed bursting in the coupled pre-B(?)tzinger neurons.The multiple time scales and two-parameter bifurcation analysis are used to explain the effects of the sodium conductance on the generation of mixed bursting.Conclusions and discussion are given in the last section.There are two conclusions on the generation of mixed bursting:the concentration of[IP3]is heavily related to the generation of mixed bursting,the concentration of[IP3]is affected by the concentration of calcium ions;the fluctuations of sodium ions can also cause the generation of mixed bursting.The methods used in this paper can provide a new idea for investigating the dynamics of mixed bursting,and it can also be applied to the study of other neuron systems with multiple timescales.