Research On Feedback Control Of Stability And Bifurcation Of Several Types Of Nonlinear Systems

Hopf bifurcation theory is a reliable tool for solving periodic solutions of differential equations.Its main theoretical value is to analyze the dynamic behavior and bifurcation direction of complex systems,and it is inseparable from the emergence of self-excited vibration phenomena in engineering.Time lag is an inevitable important factor in the control system.It can be divided into discrete time delay and distributed time lag.The occurrence of time lag makes the analysis of system stability and bifurcation characteristics more difficult.Using Hopf bifurcation theory to study various time-delay systems is a hot issue today.The specific work of this paper is as follows:1.The time-delayed feedback control problem of small-world networks is studied.The time-delay is used as the bifurcation parameter,and the stable domain and periodic solution of the controlled small-world network model are obtained.Experimental results show that the desired stability domain can be obtained by adjusting the controller parameters.2.The time-delayed feedback control problem of red blood cell system is studied.The stability of the controlled model and the Hopf bifurcation condition are given.The simulation proves that the stable region of the controlled system is expanded by adjusting the controller parameters.3.The state feedback control strategy of Caputo-fractional single gene regulatory network is studied.The system delay of the network was selected as the bifurcation parameter.The influence of order and controller parameters on system stability and bifurcation are analyzed.Finally,Stability conditions and bifurcation criteria are given.