Bifurcation Control Of Two Classes Of Fractional Delay Population Models

Fractional calculus has developed rapidly in physics,medicine,control engineering,ecology and many other fields.It has broad application prospects.Numerous studies have found that delays and phase structure are inevitable in ecology populations,and they are improvement for fractional population systems.At present,delay fractional population systems with stage structure have become a hot research topic.Based on previous work,this paper will further study two types of time delay fractional predator-prey system.This article is divided into four parts.In Chapter 1,we introduce the research background of fractional population dynamics and give some previous research results.This paper also gives the necessary preliminary knowledge for the model.In Chapter 2,in order to explore the effect of fractional order on the population,we established a prey with stage structure fractional predator-prey model.With bifurcation theory and fractional order system stability theory,we analyze the dynamic behavior of the model.The critical value of Hopf bifurcation for fractional order systems is calculated by selecting the time delay as the bifurcation parameter.When the delay is less than the critical value,the group densities tend to be stable;when the delay is greater than the critical value,The system oscillates periodically,and various group densities show periodic changes.If any two orders in the control system remain unchanged and the third order is changed,with the increase of the third order,the speed of each group density tending to the stable level will increase,and the third order has a negative correlation with the critical value of the bifurcation point.In order to control the Hopf bifurcation,we design and add a linear time-delay feedback controller.It is found that the smaller the feedback control coefficient,the slower the speed of each group density tending to the stable level.That is,the occurrence of bifurcation is postponed.In Chapter 3,considering that predators can also have a stage structure.In this chapter,two groups of predator-prey models with stage structure are established,and the time delay is used as a branch parameter.The theoretical analysis of the model is carried out.After numerical simulation,it is found that the time delay When it is less than the branch critical value,the density of various groups tend to be stable;and when the time delay is greater than the critical value,The system oscillates periodically,and various group densities show periodic changes.Then we found that changes in feedback control parameters will also affect the population density.If any three orders in the control system remain unchanged and the forth order is change,The results show that with the increase of the feedback control parameters,the density of various groups will accelerate to stabilize.In Chapter 4,This chapter summarizes and prospects the full text.