Contribution of a Ca²⁺-activated K⁺ channel to neuronal bursting activities in the Chay model

The central nervous system extensively expresses Ca²⁺-stimulated K⁺ channels, which serve to use Ca²⁺ to control their opening and closing. In this study, we explore the numerical computation of Hopf bifurcation in the Chay model based on the equilibrium point's stability and the center manifold theorem to illustrate the emergence of complicated neuronal bursting induced by variation of the conductance of the Ca²⁺-sensitive K⁺ channel. The results show that the formation and removal of various firing activities in this model are due to two subcritical Hopf bifurcations of equilibrium based on theoretical computation. Furthermore, the computational simulations are shown to support the validity of the conceptual approach. Consequently, the conclusion could be helpful to improve and deepen our understanding of the contribution of the Ca²⁺-sensitive K⁺ channel.