Houart-Dupont钙振荡模型的复杂动态

Complex dynamics in the Houart-Dupont model of calcium oscillations

运用中心流形定理和分岔理论分析了Houart-Dupont钙振荡模型的非线性动态,包括随参数变化时平衡点的类型及其稳定性的变化,从理论上严格证明了系统振荡现象产生与消失是由于平衡点发生了2次supercritical Hopf分岔导致的。通过运用matlab软件进行数值模拟,验证了理论分析结果的正确性。

This paper characterizes the nonlinear dynamics of the Houart-Dupont calcium oscillation model by using the center manifold theorem and bifurcation theory,including the stability and classification of equilibrium points.The results for the model show that supercritical Hopf bifurcations play very important roles in calcium oscillation.Numerical simulations confirm the theoretical analysis results.By combining the existing numerical results with the theoretical analysis results in this paper,a complete description of the dynamics of the Houart-Dupont calcium oscillation model has now been obtained.