The Atri intracellular calcium oscillations model was extended, and two new models were established. Furthermore, a unified model of the protein phosphorylation driven by cytosolic calcium oscillations was constructed. The numerical results obtained verified related experimental conclusions. And the analytical expressions of intracellular calcium spiral and target waves in the Xenopus laevis oocyte were obtained, resulting in velocity and waveform of calcium solitary pulse wave were found.