Regulation Of Gene Expression Model Hopf Bifurcation Analysis

In this thesis, a model of genetic regulatory system with two time delays isconsidered. Sufcient conditions for the existence of Hopf bifurcation are given.A method to determine the direction of Hopf bifurcations and the stability of thebifurcated periodic solutions. The correctness of the theoretical analysis in thisthesis are tested by a numerical example.Firstly, we employ the result due to Ruan and Wei to study the stability of thepositive equilibrium point and the existence of Hopf bifurcation of a class of geneticregulatory systems with two time delays. It is shown that Hopf bifurcation canoccur for some values of parameter. We obtained the results that delays do causesystem vibration in this model.Secondly, by using the normal form theory and the center manifold theorempresented by Hassard et al., we give a method to determine the direction of Hopfbifurcations and the stability of the bifurcated periodic solutions.