On The Dynamics Of Gene Regulatory Networks Models With Delays

Since neural networks have enormous potential in wide varieties of applications, manyspecialists and scholars have paid more attention to the research of the theory and achievemany perfect productions. Gene regulation networks are new fields in exploration of neu-ral networks. In this paper, we perform researches of dynamical behaviors of the fourclasses of gene regulatory networks model with time delays. The main contents of thispaper include: the globally asymptotically stability analysis for a class of gene regulatorynetworks with discrete delays; the stochastic stability for a class of gene regulatory net-works with distributes delays; the robustly globally asymptotically stability in the meansquare for a class of stochastic gene regulatory networks with discrete and distributeddelays; the robustly globally asymptotically stability in the mean square for a class ofMarkovian switching genetic regulatory networks with discrete and distributed delays.The main contents in this paper can be summarized as follows:1. Firstly, in the first section of the first chapter, we introduce the developmentalprocess and significance of neural networks. In the following section 2 we introduce themodels of gene networks and some results for gene networks. Then we introduce thedevelopment and new achievements for genetic regulatory networks in recent years. Insection 3, we introduce the research results for genetic regulatory networks with reaction-di?usion terms. In section 4, the organization of this paper is given.2. In the second chapter, we investigate a class of genetic regulatory networks withdiscrete delays. Under the assumption that there are equilibrium points of system, a seriesof LMIs conditions is obtained for checking the uniqueness and globally asymptoticallystability of a class of genetic regulatory networks with discrete delays by using inequalitytechniques and general Lyapunov functional. Finally, we give an example to illustrate thee?ciency of our results.3. In the third chapter, a class of stochastic genetic regulatory networks with dis- tributed delays is discussed. Firstly, we use inequality techniques and stochastic processtheory and some LMIs conditions on the the globally asymptotically stability analysis areestablished by constructing a suitable Lyapunov function. Finally, we give an example toillustrate the e?ciency of our results.4. In the forth chapter, the dynamical behaviors of a class of stochastic gene regu-latory networks with discrete and distributed delays are studied. Under the assumptionthat there is an unique equilibrium point of system, some su?cient LMIs conditions on theglobally asymptotic stability of equilibrium point are established by applying the Holderinequality and stochastic process theory. Finally, an example is given to illustrate thee?ciency of our results.5. In the fifth chapter, the dynamical behaviors of a class of Markovian switchinggenetic regulatory networks with discrete and distributed delays are studied. Under theassumption that there is an unique equilibrium point of system, some su?cient LMIsconditions on the robustly globally asymptotically stability of equilibrium point are es-tablished by applying the white noise and stochastic process theory. Finally, an exampleis given to illustrate the e?ciency of our results.