Intercellular calcium signaling allows cells to communicate with each other and to interact with adjacent cells. Gap junction is the most common and important way for cellular communication. Recently, mathematical models have been widely used to gain a precise and quantitative understanding of the dynamics of intracellular calcium ions (Ca^2＋). In this paper, we establish a mathematical model considering the gap junction permeable to Ca^2＋ and to IP${}_3$ for describing the calcium oscillations in coupled astrocytes. Store-operated calcium entry (SOCE) is viewed as the main process which controls the non-excitable cells, hence, we focus on the effect of store-operated calcium channel (SOCC) and receptor-operated calcium channel (ROCC) on the intercellular synchronization, respectively. By employing bifurcation analysis on this model, the dynamic behaviors of the coupled system with different physiological state cells is obtained with changes in the maximum capacity of the SOCC and the ROCC. The synchronization boundaries for different conditions are gained in the two parameters space of the channel parameters and the coupling strength. The results suggest that the variation of the maximum flow for different calcium channels determines the stable oscillations of the coupled system, as well as for the frequency and amplitude of oscillations. The SOCC has an expected effect on the change of the oscillatory interval while the ROCC demonstrated the influence on the amplitude modulation. Furthermore, the coupling strength and channel parameters could induce 1:1 locking of intercellular Ca^2＋ oscillations and the synchronization region like Arnol’d tongue is found.

细胞间钙信号允许细胞相互交流并与相邻细胞相互作用。间隙连接是蜂窝通信最常见和最重要的方式。最近，数学模型已被广泛用于获得对细胞内钙离子（Ca ²⁺）动力学的精确和定量理解。在本文中，我们建立了一个考虑Ca ²⁺和IP可渗透的间隙连接的数学模型。${}_3$用于描述耦合星形胶质细胞中的钙振荡。钙池操纵钙通道（SOCE）被视为控制非兴奋性细胞的主要过程，因此，我们关注贮库操纵钙通道（SOCC）和受体操纵钙通道（ROCC）对细胞间质的影响。同步，分别。通过对该模型进行分叉分析，得到了SOCC和ROCC最大容量变化时不同生理状态细胞耦合系统的动态行为。在信道参数和耦合强度两个参数空间中获得了不同条件下的同步边界。结果表明，不同钙通道最大流量的变化决定了耦合系统的稳定振荡，以及振荡的频率和幅度。SOCC 对振荡间隔的变化有预期的影响，而 ROCC 证明了对幅度调制的影响。此外，耦合强度和通道参数可以诱导细胞间钙离子的 1:1 锁定^2＋振荡和同步区域如 Arnol'd 舌头被发现。