Evaluation of bifurcation phenomena in a modified Shen–Larter model for intracellular Ca²⁺ bursting oscillations

The present work describes an evaluation of the bifurcation phenomena in a modified Shen–Larter model based on calcium-induced calcium release and inositol triphosphate (Formula presented.) crosscoupling for calcium ion (Formula presented.) bursting oscillations. A time delay for negative (Formula presented.) feedback on the (Formula presented.) receptor is added to the original Shen–Larter model, by introducing the proportion of receptors not inactivated by (Formula presented.) as a new variable. Compared with the original model, the number of chaotic regions for a stimulation level r is significantly reduced, and regions of (Formula presented.) oscillations (particularly bursting) appear to become slightly enlarged. Different topological types of bursting oscillations in this modified model are classified by fast/slow dynamical analysis and codimension-2 bifurcations of fast subsystem, when choosing better of two slow variables the free (Formula presented.) concentration in the endoplasmic reticulum and the (Formula presented.) concentration in the cytosol. Furthermore, classification and transition mechanisms of bursting (Formula presented.) oscillations could help to understand or detect more distinctive oscillatory behaviors of real cells in response to different levels of stimulation.