Bifurcation Control And Application For Several Kinds Of Delayed Systems

Hopf bifurcation,as a very common dynamic bifurcation behavior,can be used as a theoretical basis not only in stability analysis or limit cycle research,but also closely related to the self-excited vibration in practical engineering projects.In practical engineering system,time delay often appears.It is ubiquitous in engineering projects and has an impact on the robustness and bifurcation performance of the system.Moreover,because the situations encountered in real projects are very diverse and complex,it becomes more necessary to study the dynamic behavior of fractional order models.In this paper,based on the previous work of scholars,the fractional small-world network model and the network congestion model with state feedback controller will be further discussed and studied.The specific work is as follows:1.The robustness and bifurcation performance of Caputo fractional small-world network model are analyzed.The delay link in the model is taken as the bifurcation parameter for analysis,and the change of stability is observed more vividly by MATLAB simulation software.It is found that the delay affects the stability of fractional order model.2.The influence of fractional order index on dynamic behavior of fractional small world network model is analyzed.Compared with the previous integer order model,the advantage of fractional order model is found.Finally,it is found that the integer order model is a part of the fractional order model.In the actual project,the fractional order model can more accurately express the change of stability performance,which is closer to the reality.3.The problem of positive order network congestion model with state feedback control is analyzed.The stability domain and periodic solution of the system are obtained by adding state feedback controller to the uncontrolled model and changing the initial bifurcation point of the original model.The expected stability range is obtained by adjusting the parameters of the controller and the range of the parameters of the state feedback controller is given.4.The problem of integer order network congestion model with PD controller is analyzed.The stability domain of the system is obtained by adding PD controller to the uncontrolled model and changing the initial bifurcation point of the original model.By changing the parameters of PD controller,the initial bifurcation point can move forward or backward.