Bifurcation Scenarios of a Modified Mathematical Model for Intracellular Ca2+ Oscillations
JI Quan-Bao1, ZHOU Yi1, YANG Zhuo-Qin2, MENG Xiang-Ying3**
1School of Mathematics and Computational Science, Huainan Normal University, Huainan 232038 2School of Mathematics and Systems Science and LMIB, Beihang University, Beijing 100191 3Department of Biology, University of Maryland, College Park, Maryland 20742, USA
Abstract：The contribution of this work is the modification of a mathematical model for bursting Ca2+ oscillations by introducing the proportion of receptors not inactivated by Ca2+ as a new variable. Generation mechanisms of different oscillatory patterns in this modified model are investigated and classified, based on fast/slow dynamical analysis. It is shown that periodic oscillations appear around the original chaotic regions. Moreover, two new types of oscillatory phenomena are observed at the sustaining region. The results may be instructive for understanding the difference between direct observation of dynamical behavior in real cells and theoretical explanations under a variety of stimulus conditions.
2015, Vol. 32 
