2013•International Journal of Bifurcation and ChaosRequires access

HOPF BIFURCATION IN A CALCIUM OSCILLATION MODEL AND ITS CONTROL: FREQUENCY DOMAIN APPROACH

Yu Chang, Lili Zhou, Jinliang Wang

Abstract

The Hopf bifurcation in a calcium oscillation model is theoretically analyzed by Hopf bifurcation theory in frequency domain. Approximation expressions for frequencies and amplitudes of periodic orbits arising from Hopf bifurcation are provided by using second-order harmonic balance method. In addition, a new method is proposed to control the amplitudes of the periodic orbits. Numerical simulations show the effectiveness of the method for suppressing periodic oscillations.

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Key concepts: Hopf bifurcation, Harmonic balance, Homoclinic bifurcation, Mathematics, Biological applications of bifurcation theory, Saddle-node bifurcation, Mathematical analysis, Oscillation (cell signaling)