Study On Bifurcation And Control Of Genetic Regulatory Networks

Systems biology is a typically rising inter-discipline in the 21 st Century. The genetic regulatory network is a kind of basic and important biological network in biological engineering research. The complex dynamics of genetic regulatory networks is a key problem in the process of gene expression and regulation and it has become an important topic in the engineering theory and application in biology.In this dissertation, the genetic regulatory network is based on the differential equation model. By using the bifurcation theory and state feedback control method, we study the stability and the Hopf bifurcation control of the model. The main works and contributions are as follows:Firstly, a state feedback method is proposed to control the Hopf bifurcation for a single-gene expression model. The sum of the delays is chosen as the bifurcation parameter. Without control, the bifurcation will occur early when the sum of the delays passes through a certain value. However, under the control of the state feedback, the onset of the critical value of the undesirable Hopf bifurcation is postponed, and thus the model can remain stable for a larger delay.Then, the bifurcation of a triple-gene expression model is discussed. We take a single-gene oscillator as a node and a ring network can be formed under the interaction of genes. Under the linear transformation, the characteristic equation of the system can be obtained and the distribution of the roots of the characteristic equation is analyzed based on Routh-Hurwitz stability criterion, and the condition of the bifurcation is derived. It is verified by the numerical simulations that the Hopf bifurcation occurs when the sum of the delays pass through a critical value.Finally, the state feedback scheme is designed for a triple-gene expression model to delay the onset of the bifurcation. The sum of the delays is chosen as the bifurcation parameter. Under the controller, the model can remain stable in a domain of larger delays. Therefore the object of the bifurcation control is realized.