Dynamics of in-phase and anti-phase bursting in the coupled pre-Bötzinger complex cells

Abstract

Activity of neurons in the pre-Bötzinger complex within the mammalian brain stem has an important role in the generation of respiratory rhythms. Previous experimental results have shown that the dynamics of sodium and calcium within each cell may be responsible for various bursting mechanisms. In this paper, we study the bursting dynamics of the two-coupled pre-Bötzinger complex neurons. Using a combination of fast-slow decomposition and two-parameter bifurcation analysis, we explore the possible forms of dynamics that the model network can produce as well the transitions of in-phase and anti-phase bursting respectively.

Appendix

For $x\in \{s,m_P,m,h,n\}$, the function ${x}_{\infty }(v)$ takes the form ${x}_{\infty }(v)=\{1+ exp[(v-{\theta }_{x})/{\sigma }_{x}]\}^{-1}$, and for ${x}\in {h,n}$, the function ${\tau }_{x}(v)$ takes the form ${\tau }_{x}(v)$= ${\tau }_{x}/cosh[(v-{\theta }_{x})/2{\sigma }_{x}]$. The parameter values are listed in the Table 1.

Table 1 Parameter values used in the model