Stability And Hopf Bifurcation Analysis Of Two Kinds Of Genetic Regulatory Network With Time Delay And Diffusion

The genetic regulatory network is a network model based on gene activities in real organisms and abstractly generalizes the regulatory relationships among genes.Because the regulatory relationship between genes is dynamic,the whole network system may produce complex dynamic behavior.At present,the study on the dynamics of gene regulatory networks is of great practical significance to biomedicine and has become a hotspot of current research.In the actual process of gene regulation,such as transcription,translation,replication and so on,such biochemical reactions need time to complete,and the influence of time delay factors on the dynamics of the whole genetic regulation network system cannot be ignored.In addition,due to the spatial structure of the gene network inside the cell,the material concentration distribution is not uniform,so the gene products may transfer from the high concentration area to the low concentration area and cause diffusion effect.Therefore,it is necessary to consider the influence of diffusion effect on the system.Based on the above discussion,this paper mainly studies the stability and Hopf bifurcation of two types of genetic regulatory networks with time-delay and diffusion characteristics.It mainly includes the following aspects:(1)Stability and oscillation analysis of genetic regulatory networks with multiple time delays and diffusion ratesIn the genetic regulatory network,the diffusion rate of gene-related products plays an important role in the regulation mechanism of gene expression,especially in transcription and translation.However,the effect of diffusion rate on gene oscillation expression is not clear.By considering the diffusion rate of protein and m RNA,combined with the time delay of biochemical reaction,a new model of genetic regulation network was constructed.Then,two important problems of the system,namely stability and oscillation,are solved in detail.In addition,the properties of the oscillations are further studied.The results show that the time sum of biochemical reaction will affect the stability of the positive equilibrium point,resulting in the oscillation.The diffusion rate of protein and m RNA has an important effect on the oscillation characteristics.Finally,the results of the analysis were verified by numerical simulation,and it was found that a small change in diffusion rate could lead to a large change in the expression of oscillating genes.(2)Hopf bifurcation analysis of the p53-MDM2 genetic regulatory network with time-delay diffusion characteristicsFirstly,time delay and diffusion effect were introduced into the p53-Mdm2 negative feedback regulation network to establish a more complete network model.The two main problems of gene regulation network,namely the stability and oscillation of the system,are analyzed in detail.The conditions of local stability and Hopf bifurcation generation of the system are deduced by the algorithm.It is proved that gene expression is not only dependent on the delay of transcription and translation,but also affected by the diffusion coefficient,which may lead to periodic oscillation.The results show that the time delay of gene product regulation reaction plays an important role in the stability and oscillation of the system,and the influence of diffusion effect on the dynamics of the system can not be ignored.In addition,the direction of Hopf bifurcation and the stability of bifurcation period are studied by using the gauge type theory and the central manifold theorem.Finally,the theoretical results are verified by numerical simulation.simulation.