Stability,Bifurcation Analysis And Synchronization Control Of Genetic Regulatory Networks

Genetic regulatory networks are complex biological networks that describe the genetic activities and the regulatory relations among the genes based on the dynamical models.In recent years,the genetic regulatory networks have received a lot of attention due to the increasingly extensive application in the fields of the genetic engineering and the science of information biology.Genetic regulatory networks are able to model many body's cells,such as phage cells,cellular clock and tumour cells.The phenotypic character originates in the dynamic features of genetic networks.The genes in networks regulate the genetic expressions by products,which make the whole networks present self-organized stability and bifurcation.By mutual cooperation,the clusters of networks present cooperative behaviors,such as synchronization.Exploring the stability and bifurcation of genetic regulatory networks and the synchronization of the clusters of genetic networks is important and meaningful for studying the underlying mechanism of biological features from the cellular level and understanding the living phenomena.Based on the theories of characteristic equation and combining with the techniques of dynamic analysis for discrete systems,the theories of fractional differential and diffusive systems,and the analysis method of bifurcation,this dissertation investigates the stability and bifurcation for the integer-order discrete model of genetic regulatory networks,the time-fractional model with diffusion and the delay-coupled model of genetic regulatory works with the hub structure,respectively.Meanwhile,this dissertation designs the schemes of event-based control and aperiodically adaptive intermittent control for the coupled genetic regulatory networks,which drive the networks to reach the goal of cluster synchronization.The main work of this dissertation is outlined as follows:Multiple bifurcation and chaos of an integer-order and discrete genetic regulatory network.This dissertation proposes a first-order and discrete genetic model,and study the stability of the fixed points,the bifurcation and chaos of the networks.For the different fixed points,by taking the biological parameters and the discretized step size as bifurcation parameters,the conditions of the emergence of fold bifurcation,flip bifurcation and Neimark-Sacker bifurcation are derived,respectively,The simulation results shows that as the step size increases,this model presents multiple orbits with different periods and chaos,and it is confirmed that the developed discrete model has richer dynamics than that of the corresponding continuous model.It provides theoretical references for the application of genetic model to computer simulation.Stability and Hopf bifurcation of fractional genetic regulatory networks with diffusion.This dissertation develops a genetic network model with time-fractional differential and Laplace operator,analyses the number of the equilibria and study their local stability and Hopf bifurcation.In the cases that diffusion is absent and present,the conditions of local stability in terms of the biological parameter and the spatial parameter are given.Both the Hopf bifurcation and the frequency of oscillation are analyzed.The relationship between the stability region,amplitude and the fractional order is revealed by the simulations,which contribute to understanding the influence of the fractional order and diffusion on the dynamics of the genetic regulatory network.Stability and Hopf bifurcation of delay-coupled genetic regulatory networks with the hub structure.The hub structure in a sense reflects the difference of the link relations of gene nodes.For the network consisting of two hub-structured modes with delay-coupling,the local dynamics is studied.The existence and number of the equilibrium are analyzed,and the stability domain and bifurcation condition are obtained.The obtained results have shown the different effect of the coupling delay on the stability of the network under different biological parameters.Cluster synchronization of coupled genetic regulatory networks and even-based control.The issue of cluster synchronization control is studied for the model of coupled genetic networks.Taking advantage of the feature of cluster synchronization,this dissertation designs the improved event-triggered scheme,which deals with the states of neighbors in intra clusters and extra clusters in individual ways such that the linking matrix is reduced to be used.Meanwhile,it does not require the neighbors' information in real time,which avoids continuous transmission of information and the emergence of Zeno behavior.The cluster synchronization criterion is established,and the range of the triggering gains for cluster synchronization are given by way of constructing the coupling matrix and control gains.Cluster synchronization of coupled and delayed model of genetic regulatory networks and the aperiodically adaptive intermittent control.The cluster synchronization is further investigated for the coupled genetic networks with time-varying delay.In view of the fact that the discontinuous link of networks can lower energy-consumption,this dissertation establishes a delayed model with the coupling that intermittently occurs and the intra-cluster coupling strength is adaptively adjusted,and proposes the aperiodically adaptive intermittent control strategy,which relaxes the demand of the connectivity of the intra-cluster coupling topology.In two cases of delays,the cluster synchronization criteria are got in terms of the lower bound of the aperiodical time-span and the maximum ratio of the un-controlling time.The scheme removes the limit on the relationship of the bound of the delay and the bound of the controlling time,and helps reaching the goal of cluster synchronization.Finally,the work of this dissertation is generalized and summarized,and the issues of future study are proposed.