The dynamics of an astrocyte model is investigated. The astrocytes represent a type of glial cells regulating oscillations of major signaling cells, e.g. neurons. Subserved by complex molecular mechanisms the astrocytes generate calcium auto-oscillations which, in turn, are associated with the release of neuroactive chemicals into extracellular space. At variance with classical astrocyte models the three-component model considered takes into account a regulation of calcium release due to nonlinear dynamics of inositol-1,4,5 trisphosphate (IP3).