Dynamical Of Gene Network With SUM Regulatory Logical

Life system is the results of a lot of basic units, such as gene,protein and metabolic products, which are essentially discrete. The first step of this research method is how to integrate all kinds of biological databases and give a model as correctly as possible. To solve this problem will meet with many problems of computational mathematics and statistics, for example, how to integrate the data of different databases, how to deal with the model based on a small quantity of data. There are a great deal of work on this aspect. Summarizing the researches, we find that the large-scale dynamical network is the most appropriate model. That is to say, life phenomenon must be cognised on the complex system composed by thousands of biological molecules. While the interaction of these thousands of biological molecules show character of network structurally. Therefore, life science is faced with a new transitional period that we should cognise life activity of bivalves based on the structure and function of network composed by biological molecules.The previous work of system biology focused on the construction of the special gene network and experiments, such as toggle switch consists of two negative feedback and the repressilator consists of three genes connected in a feedback loop, and there is little result on the synthetic biology, cell dynamics simulation, construction and control strategies of gene networks, discovery of technical.We studied the various levels of structure present in the biology system by the nonlinear analysis and combining of biological information resources and discussion the nonlinear biological systems with multi-scale, time-delay and noise for theoretical of gene regulatory or pharmaceutical. Moreover, It is can be used for the improvement of the biology experimental design and construction of synthetic biological. In this thesis,we mainly study two aspects of dynamical of gene network with SUM regulatory logical. One is the periodic oscillation in delayed gene regulatory network with SUM regulatory logical and small perturbations. The other one is robustness of interval gene networks with multiple time-varying delay and noise. Then we introduce the main contents and innovate points of this paper, which can be listed as follows.(1) A cellular system is generally characterized with significant time delays in gene regulation, in particular, for the transcription, translation, diffusion, and translocation processes. Moreover, periodic perturbations are widespread in the environment. Such time delays and perturbation may affect the dynamics of the entire biological system, both qualitatively and quantitatively.In the second section, we derive new criteria for evaluating the global stability of periodic oscillation for gene networks with small perturbation and distributed delay, and lager time scales reaction. We results relay on the of Lipschtiz conditions of Hill function, topology of gene regulation networks and delay kernels. In particular, our method based on the proposed model transforms the original network into matrix analysis problem, thereby not only significantly reducing the computational complexity but also making analysis of periodic oscillation tractable for even large-scale nonlinear networks.(2) The small number of reactant molecules involved in gene regulation can lead to significant fluctuations in intracellular mRNA concentrations, and there have been numerous recent studies devoted to the consequences of such noise at the gene regulatory level. Besides, a cellular system is generally characterized with significant time delays in gene regulation, in particular, for the transcription, translation, diffusion, and translocation processes. Such time delays and stochastic noises may affect the dynamics of the entire biological system, both qualitatively and quantitatively. Moreover, all mathematical models for a biological system involve interval parameters due to the modeling errors, measurements errors, and liberalization approximations. Therefore, it is imperative and of prime importance to consider stochastic effects of the stability property on the interval GNs with time varying delays, to gain deep insight into the essential mechanism of the bimolecular systems.In the third section, we investigated the robustness of the gene networks with noise perturbations and time varying delays, which shows the stochastic interval GN stable in the mean square even with time varying delays if the linear matrix inequality holds. Our theoretical results were derived in the form of LMIs, which is very easy to be verified and also no tuning of parameters is required.At last, a compact summary of this paper is given by combining the advances of the previous researches in this fields and our work. The prospect for future study is also given.