We investigate the various types of complex Ca2+ oscillations which can arise in a model based on the mechanism of Ca2+-induced Ca2+ release (CICR), that takes into account the Ca2+-stimulated degradation of inositol 1,4,5-trisphosphate (InsP3) by a 3-kinase. This model was previously proposed in the course of an investigation of plausible mechanisms capable of generating complex Ca2+ oscillations. Besides simple periodic behavior, this model for cytosolic Ca2+ oscillations in nonexcitable cells shows complex oscillatory phenomena like bursting or chaos. We show that the model also admits a coexistence between two stable regimes of sustained oscillations (birhythmicity). The occurrence of these various modes of oscillatory behavior is analysed by means of bifurcation diagrams. Complex oscillations are characterized by means of Poincaré sections, power spectra and Lyapounov exponents. The results point to the role of self-modulation of the InsP3 signal by 3-kinase as a possible source for complex temporal patterns in Ca2+ signaling.