Stability Analysis And Bifurcation Control Of Several Classes Of Fractional Order Systems

Hopf bifurcation theory is a powerful tool for solving periodic solutions of differential equations.It has important research value for analyzing the dynamic characteristics and periodic oscillation of complex networks.At the same time,there are various forms of delay in gene regulatory networks and erythrocyte systems,mainly in the form of discrete and distributed delays which can greatly change the stability and bifurcation characteristics of the system.Because of the complexity of the system in practical engineering,the state-space expression is described more accurately by fractional order form.Therefore,it is very meaningful to study the bifurcation behavior of fractional-order time-delayed systems.In this paper.We use bifurcation theory to study fractional order theory,distributed time delay and time delay feedback control.1.The bifurcation dynamics of gene regulatory networks with distributed delays are studied.We choose the time delay as the bifurcation parameter to discuss the effects of different distributed cores.Finally,the different derivation and simulation diagrams of strong and weak cores are given.2.The stability and periodic oscillation of Caputo fractional-order gene regulatory network with SRNA are studied,and we discuss the effects of different fractional-order on the bifurcation behavior of the whole system.The results show that the bifurcation parameter of the system increases nonlinearly as the fractional order decreases.3.The problem of time-delay feedback control for Caputo fractional order erythrocyte system is studied.We use the time-delayed feedback controller to change the initial bifurcation point of the original system to obtain the stable region and periodic solutions of the system,which is suitable for engineering requirements.We have successfully obtained the desired range of stability region and given the range of the parameters of the controller by adjusting the parameters of the controller.