Hopf bifurcation control of calcium oscillations in hepatocytes

This paper discusses a problem of the Hopf bifurcation control for a mathematical model of intracellular calcium oscillations by calculating the curvature coefficient of limit cycle and the bifurcation control theory. We find that the appearance and disappearance of calcium oscillations in this system are due to the supercritical and subcritical Hopf bifurcation of equilibrium points, respectively. In addition, a nonlinear feedback controller is proposed to control the frequency and amplitude of periodic orbits arising from the Hopf bifurcation. Numerical analysis and simulation results are carried out to illustrate the validity of the feedback controller in controlling Hopf bifurcations.