时滞基因调控模型的稳定性与Hopf分支

Stability of a Gene-regulatory Model with Time Delay and Its Bifurcation

摘要:

研究时滞因素对基因调控模型的正平衡点的稳定性的影响及其诱发的周期振荡，包括离散时滞和分布时滞两种情形。通过分析相应的特征方程根的分布，得到了系统正平衡点绝对稳定、条件稳定的条件以及时滞诱发周期振荡的临界值。最后，通过数值模拟验证了理论分析结果的正确性。

Abstract:

An investigation was made into the effect of the time delay on the stability of the positive equilibrium of the gene-regulatory in cells and the periodic oscillatory phenomenon induced by it. Two cases of discrete and distributed delay were studied. By analyzing the associated characteristic equation, the conditions for absolute stability and conditional stability as well as the critical values of inducing periodic oscillation were obtained. At last, the numerical simulations were employed to support the theoretical results.