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Complex Dynamics in the Kummer-Olsen Model of Calcium Oscillations

Oscillations of cytosolic calcium concentration, known as calcium oscillations, play a vital role in providing the intracellular signalling. These oscillations are explained with a model based on calcium-induced calcium release (CICR). The nonlinear dynamics of the Kummer-Olsen calcium oscillation model is discussed by using the center manifold theorem and bifurcation theory, including the variation in classification and stability of equilibria with parameter value. It is concluded that the appearance and disappearance of calcium oscillations in this system is due to supercritical Hopf bifurcation of equilibria. Finally, numerical simulations are carried out to support the theoretical analysis of the research. By combining the existing numerical results with the theoretical analysis results in this paper, a complete description of the dynamics of the Kummer-Olsen calcium oscillation model has now been obtained.