Dynamical analysis of bursting oscillations in the Chay-Keizer model with three time scales

Based on the Chay-Keizer model with three time scales, we investigate the role of the slowest variable in generating bursting oscillations in pancreatic β-cells. It is shown that both of the two slow processes can interact to drive fast, medium and slow bursting oscillations typically observed in pancreatic β-cells. Moreover, diverse patterns of electrical bursting are presented, including the “fold/fold“ bursting, “fold/homoclinic“ bursting, “fold/Hopf“ bursting via “fold/fold“ hysteresis loop, and the “fold/fold“ bursting via point-point hysteresis loop. Fast-slow dynamics is used to analyze the types and generation mechanisms of these bursting oscillations. The results can be instructive for understanding the role of the slow variables and the current conductance in pancreatic β-cells activities.

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