Dynamical Analysis of a Calcium Oscillation Model in Non-Excitable Cells

Yi Zhou; Zheng Fei Wu; Yu Hong Huo

doi:10.4028/www.scientific.net/AMM.226-228.521

Paper Titles

Aeroelastic-Acoustics Numerical Simulation Research
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Complex Dynamics in the Kummer-Olsen Model of Calcium Oscillations
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Hopf Bifurcation and Numerical Simulation in a Calcium Oscillation Model
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Analysis of Attitude and Dynamics Characteristic of a Kind of Submerged Buoy
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Dynamical Analysis of a Calcium Oscillation Model in Non-Excitable Cells
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Simulation Research on Defects Detection in Straight Pipes Using Guided Waves
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Bifurcation Induced by Mass Variation in Piecewise Linear System
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Simulation on Shock Wave Propagation in Metallic Foams Subjected to Impact Loading
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Nonlinear Dynamics of Simple-Supported Beam under Concentrated Moving Load
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HomeApplied Mechanics and MaterialsApplied Mechanics and Materials Vols. 226-228Dynamical Analysis of a Calcium Oscillation Model...

Dynamical Analysis of a Calcium Oscillation Model in Non-Excitable Cells

Abstract:

The Borghans-Dupont model of calcium oscillations based on both the calcium-induced calcium release and calcium-activated inositol trisphosphate concentration degradation is considered. Dynamical effect of the stimulation level on the calcium oscillation behavior is studied. The qualitative theory of differential equations is used to explain the mechanism of these oscillations. We investigate the existence, types, stability and bifurcations of the equilibria by applying the centre manifold theorem, stability theory and bifurcation theory and prove that oscillations are due to supercritical Hopf bifurcation. Finally, we perform numerical simulations, including time courses, phase portraits and bifurcation diagram, to validate the correctness and the effectiveness of our theoretical analysis. These results may be instructive for understanding the role of the stimulation level played in complex dynamics in this model.