Dynamic Analysis Of Two Types Of Biological Networks

With the development of bioinformatics, the research of biological network theory and its application has become the frontier topics in the fields of biologi-cal mathematics, information science and automation control. Among them, the dynamics analysis of neural network and genetic regulatory network has been the research hot topic and difficulty all the time. Artificial neural network has important theoretical and practical value in chaotic secure communications, network optimiza-tion and control, artificial intelligence, Military informatics and pattern recognition fields. For more convenience in computer applications, this paper study the exis-tence uniqueness and global exponential stability of periodic solution for high-order discrete-time Cohen-Grossberg neural networks with time delays. In addition, ge-netic regulatory network is an important content of current bioinformatics research, mainly reveal the complicated life phenomenon from the angle of the interaction between genes. In this paper, we study the finite-time stability of genetic regula-tory network with impulsive effects. The main content of this paper is arranged as follows:In chapter 1, we will review the development of a couple of typical biological networks history and introduce the biological basis of high-order neural networks and genetic regulatory networks, moreover, the studying status quo on a couple of typical biological networks and its research significance are summarized systematically.In chapter 2, we research the existence and global exponential stability of equi-librium for high-order discrete-time Cohen-Grossberg neural networks with time de-lays. Through the application of the Young's inequality, we obtained some sufficient conditions to ensure the existence of the model's equilibrium or periodic solution without assuming the bounded- ness of signal transmission functions. And then, the criterion for the global exponential stability is given using Lyapunov method.In chapter 3, some sufficient theorems are obtained for ensuring the finite-time stability of genetic regulatory networks with impulsive effects. In addition, by using linear matrix inequality and constructing suitable Lyapunov function, some sufficient criterions which ensure the finite-time stability of genetic regulatory networks with impulsive effects.Finally, the fourth chapter summarizes the research work of this dissertation and provides some trends of future research.