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Bifurcation Control And Applications For Several Classes Of Fractional Dynamical Systems

Posted on:2019-01-11Degree:MasterType:Thesis
Country:ChinaCandidate:Q S SunFull Text:PDF
GTID:2428330566999396Subject:Control engineering
Abstract/Summary:PDF Full Text Request
As a generalization of general integer order calculus,fractional calculus is an important branch of the field of mathematics.In recent years,the theory of fractional calculus has been successfully applied to various fields.People gradually find that fractional calculus can accurately describe some non classical phenomena in natural science and practical engineering applications,which has caused considerable research fever.A large number of research literatures show that in actual network applications,time delay is an unavoidable problem.In fractional order systems,time delay is closely related to the dynamics of the system.In the last ten years,the dynamic behavior analysis of delayed fractional systems has become a hot research topic,including stability,bifurcation,control,synchronization and so on.Based on previous studies,we will further explore the dynamics of the two networks of fractional genetic regulatory network and fractional survival red blood cells model.At present,there are few theoretical results about the Hopf bifurcation in these fractional order models.In this paper,we will focus on the stability and bifurcation control of the delayed fractional systems.The following work is as follows:1.The stability and bifurcation of a class of delayed fractional-order single genetic regulatory network is studied.In the fractional single genetic regulatory network,we first choose the total time delay as the bifurcation parameter,then we analyze the dynamic behavior of the fractional delayed single genetic regulatory network,get the delayed dependent stability criterion,and give the bifurcation condition.The relation between the fractional order's value and the critical bifurcation value of the time-delay is also given.It is found that the time delay affects the stability of the genetic network and the fractional order affects the time of the bifurcation.2.we discuss the stability and bifurcation control problem of a fractional-order survival red blood cells model.First,we choose time delay as bifurcation parameter,then linearize the model,get its characteristic equation,analyze and get the condition of Hopf bifurcation.It is found that the fractional order's value has a relationship with the bifurcation point of the fractional system,and the higer the fractional order's value is,the more early the bifurcation occurs.Secondly,in order to control the dynamic properties of the fractional survival red blood cells model,a fractional PD controller is designed and applied to the model.The controller can better control the dynamic behavior of the system.By adjusting the parameters of fractional PD controller,we can control the dynamic behavior of the system and get the ideal stability region.
Keywords/Search Tags:Fractional-order, Time delays, Stability, Hopf bifurcation, Bifurcation control
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