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Abstract

With the rapid development of bioinformatics , genome informatics research in the study of gene regulatory networks become one of the main themes , and has formed a new area of ??research , mathematics , information science , computer science , molecular biology , and many other subjects of mutual penetrate the formation of cross- disciplinary study of gene regulatory networks from the level of the genome reveals life growth , movement mechanism , through research can be deep - level understanding of life activities of law . so on gene regulatory networks important role and nature has gradually in recent years, systems biology the hotspot research one . analyze and summarize existing work based on the combination of biological knowledge and mathematical knowledge , the stability of a class in the field of bioinformatics gene regulatory networks described by differential equations sexual made ??a preliminary analysis in view of the special structure of gene regulatory networks described by differential equations , the first use of the Banach contraction mapping principle to prove the existence and uniqueness of the equilibrium position of gene regulatory networks ; further solved to obtain the equilibrium position of the structure approach and the use of the traditional iterative method to prove the existence and uniqueness of the equilibrium position of gene regulatory networks . Based on this , the use of the Lyapunov method to study the stability constant gene regulatory network equilibrium position , including asymptotic stability , exponential stability given some practical sufficient condition ; stability of the equilibrium position of the gene regulatory network analysis of the time-varying asymptotic stability and exponential stability , given the same number of simple sufficient criteria ; Finally, the use of the Lyapunov method combined with linear matrix inequalities , a brief discussion of the stability and asymptotic stability of delay gene regulatory network equilibrium position .

Qualitative Analysis of a Gene Regulatory Network

Abstract

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