Stability and Hopf Bifurcation of a Class of Genetic Regulatory Network with Multiple Delays

Gene expression can be divided in transcription and translation, the genetic regulatory network describes this process appropriately. Stability and Hopf bifurcation of two-gene regulatory network with multiple delays is studied in this paper. Firstly, the model with multiple delays can be introduced and the conditions of stability are given in positive equilibrium
$(M_{1}^{*},\ P_{1}^{*},M_{2}^{*},\ P_{2}^{*})^{T}$
. Secondly, because of the actual significance of gene expression, different time delay is utilized as bifurcation parameter to discuss the stability and Hopf bifurcation. By analysis, the relationship between the two delays have also been provided. Then, in order to validate the effectiveness of theories, two numerical examples can be used. The conclusion has been presented in final.