Bifurcation Analysis and Transition Mechanism in a Modified Model of Ca²⁺ Oscillations

Some new elements are introduced into a mathematical model of intracellular calcium oscillations, which make it particularly suitable for the study of bifurcation. In addition to generating regular oscillations, such a modifed model can be used to reproduce the burst discharges similar to those recorded in experiments and to describe two new types of oscillatory phenomena. By means of a fast/slow dynamical analysis, we explore the bifurcation and transition mechanisms associated with two types of bursters due to changes in the interaction of two slow variables with different timescales.