Complex Dynamics Analysis And Controller Application Based On Time-delay Model

Hopf bifurcation theory is an important branch of bifurcation theory,which has important research value for analyzing the dynamic characteristics and periodic oscillation of complex networks.Many kinds of time delays exist in most complex network systems.The addition of time delay changes the dynamic characteristics of the original system,such as stability,bifurcation,chaos and so on.At the same time,based on the complexity diversity of the system in practical engineering,researchers often use fractional order theory to analyze the complex system.Based on bifurcation theory,this paper studies fractional order theory,leakage delay and delay feedback control,etc.The specific work is as follows:1.The study and establish of Goodwin model with leakage delay,take leakage delay as the bifurcation parameter,use some mathematical knowledge to discuss and analyze the dynamic effects of different leakage delays on the system,and obtain the local stability of Goodwin model and the existence of Hopf bifurcation.2.The study of bifurcation dynamics of a single gene regulatory network model with pd controller,study the existence,uniqueness and stability of its equilibrium point or periodic solution,and give a series of global stability conditions that are easy to verify.The influence of PD controller on bifurcation model of single gene regulation network is revealed,the bifurcation mechanism of complex dynamic behavior changing with fractional order or time delay is clarified,and a practical algorithm for determining bifurcation direction is given.3.The study of Fractional order small world network model that balance or the existence,uniqueness and stability of periodic solutions,given a series of easy to verify the global stability conditions,reveal the fractional order time,time delay and the coupling way for complex bifurcation model the influence law of small world network,clear complex dynamic behavior with the number of points order or delay changes of bifurcation mechanism,determine the direction of the bifurcation and practical algorithm,based on the understanding of mechanism of bifurcation,determine the key characteristics of network bifurcation,PD control strategy is put forward,realize the goal of bifurcation control.The response of control gain to bifurcation threshold,amplitude and frequency of bifurcation periodic solution is also given.