Global Exponential Stability Analysis Of Several Types Of Time-delay Gene Regulatory Networks

At present,one of the main research hots of genetic regulatory networks is to study the internal mechanism of genetic regulation networks by establishing mathematical models.At the same time,the different genetic regulatory network models can be used to quantitatively describe the dynamic behavior of different biological systems,which is more helpful to find out the mechanism of interaction between genes.So,it is very important to establish a reasonable and effective network model to better study the genetic regulation networks.This thesis mainly studies the global exponential stability of three classes of coupling gene regulatory networks with constant delays.Firstly,study the global exponential stability of coupling cycle genetic regulatory networks with constant delays.Above all,the Brouwer's fixed point theorem is used to prove the existence of nonnegative equilibriums.On this basis,a new method is proposed to establish the global exponential stability criteria of the considered system.Numerical examples are given to check the validity of the criteria.Secondly,the global exponential stability of time-delay coupled genetic regulation networks with two central structures is studied.The Brouwer's fixed point theorem are employed to prove that the system under consideration has at least a nonnegative equilibrium.On this basis,the global exponential stability criteria are derived.The delay-dependent and independent stability criteria are obtained,and finally,numerical examples show the effectiveness of the criteria.Thirdly,study the global exponential stability of time-delay coupled genetic regulatory networks with a cycle structure and a central structure.The stability criterion which are dependent and independent on exponential decay rate of exponential decay rate are given respectively.Numerical examples show the effectiveness of the criteria.