Bifurcation Control And Applications For Several Kinds Of Delayed Systems

Hopf bifurcation is an important dynamic bifurcation problem,which not only has theoretical value in the study of dynamic bifurcation and limit cycle,but also has a close connection with the generation of self-excited vibration in engineering.It is a common phenomenon in engineering.Numerous researches indicate that due to the time required for information interaction and network node adjustment,the time delay is usually inevitable in a large number of actual networks.However,the time delay has a very important influence on the dynamic behavior of the network,so it is meaningful to study the dynamic behavior of networks with time delay.At present,the Hopf bifurcation of time-delayed networks has become a hot research topic,including stability,synchronization,control and so on.Based on the previous research work,this paper will further investigate the dynamics of the neural network and fractional double gene regulation network with many kinds of delays,and look into the bifurcation control problem of genetic networks and small-world networks.Specific works are as follows:1.The fractional-order genetic regulation network model with two genes is established.The time delay of the network is selected as the bifurcation parameter,and the stability and bifurcation of the network are analysed.The research shows that the delay affects the stability of the fractional network.2.The stability and bifurcation of the network consisting two neurons with discrete and distributed delays are considered.The discrete delay of the network is selected as the bifurcation parameters,and the stability and Hopf bifurcation of the network are analysed.It is found that the discrete delay has an important impact on the stability of the network.3.The method of the PID bifurcation control is discovered,and the problem of bifurcation control of gene regulation network and small-world network based on PID control strategy is discussed.The time delay is taken as the bifurcation parameter,and the effect of PID controller on the stability and Hopf bifurcation of these networks is analysed.The study shows that the dynamic performance of the network can be effectively improved by adjusting the controller parameters.4.The design method of PID control strategy based on the configurable balance point of the small world network is proposed.The control strategy can stabilize the controlled small-world network at the preset equilibrium point,and the dynamic behavior of the control network is improved.