Qualitative Analysis Of Gene Regulatory Network Models

It is possible to determine gene regulatory network with the rapid development of bioinformatics and the emergence of DNA chip technology. The gene regulatory networks have become a new field of bioinformatics and biomedical research, and the study of gene regulatory network theory and experiment has caused more and more attention. the gene regulatory network is a dynamic biochemical system which mainly describe the gene product, such as highly complex interaction between protein and m RNA. Thus, it is greatly significance for people to understand how genes and proteins work and form a complex network which can realise all kinds of biological function. For example, it makes the gene of zebrafish synthetise the function of the protein in the cell due to the effect of regulation of the gene, these proteins form skin tissue by orderly arrangement, then, the body pattern is formed. So it is very significant to understand the pattern formation of zebrafish from gene level. Based on the analysis and summary of gene regulatory network model by s RNA adjust with delay and the research situation of zebrafish model, researching the dynamic behavior of the above two models respectively through the analysis of the stability theory, and the theory of Turing bifurcation. The paper is organized as follows:The first chapter elaborates the gene regulatory networks system with delay, zebrafish model with delay and cross-diffusions, the status and progress are studied. The main content of this paper is expounded.The second chapter establishes a gene regulatory network model with delay, Selecting delay as the bifurcation parameter, it discusses local asymptotic stability and Hopf bifurcation of the system.The third chapter studies the zebrafish model with cross-difussion, analyzing the Turing unstability, decucing the coefficients of amplitude equation, and Turing pattern selection and stability are discussed.The fourth chapter talks about the zebrafish model with delay and cross-diffusion, Selecting delay as the bifurcation parameter, Turing instability is analyzed, and discussing the effect of delay on pattern selection.The fifth chapter summarizes the rearch work of this dissertation. Furthermore, the future research direction is made.