Qualitative Analysis Of A Gene Regulatory Network

Along with the rapid development of bioinformatics, gene regulation network has become a in post-genome era new research topic in post-genome era. It is a cross subject with mathematics, informatics, computer science, molecular biology.A study on gene regulation network is to reveals life growth, movement mechanism at the genome level, by which the deeply understanding of life activity rule can be achieved. Therefore, the research on gene regulation networks has gradually become the hot topic of systems biology in recent years.In the analysis and summary on the basis of existing related work, combining with biology and mathematics knowledge, a preliminary analysis on the stability of a class of gene regulation network which is described by differential equation is studied.In consideration of the special structure of the differential equation, , Based on the theory of compressed image the existence and uniqueness of the equilibrium of the gene regulation network is firstly proved. Further, the traditional iteration method is applied to obtain the constructive method of the solution.Then based on the Lyapunov stability theory, several sufficient conditions on the stability of gene regulation network are obtained, including asymptotic stability, exponential stability. Finally using Lyapunov method and combining linear matrix inequality, the stability of equilibrium position and asymptotic stability of time-delay gene regulation network are discussed .