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

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.