Hopf Bifurcation And Control Of Time-dely Complex Networks

The research on complex networks is very extensive,especially on the control and analysis of bifurcation and chaos of complex networks.The research on system properties can provide scientific theoretical guidance for our production and life.Complex networks not only widely exist in nature,such as neural network,food chain network,etc.,but also in human society,such as the Internet,Internet of things,transportation network,financial network,power network,communication network and so on.The first two chapters describe the knowledge and theory of bifurcation and chaos of complex networks and the general situation of their development,including the theoretical knowledge we used in the research process of this paper,as well as the content of the main work of this paper.In chapter 3,we present a three-dimensional network model with continuous distributed delay.The stability of routhhurwit criterion was analyzed.The local asymptotic stability condition of the system is obtained.We take a parameter as a variable and find that the time division phenomenon occurs when it passes a value.By using some theories,such as central manifold theorem and normal form theory,we obtain the bifurcation direction,bifurcation periodic solution and bifurcation stability quasi.Finally,we use the mathematical software in several cases of data simulation,the results are verified.In chapter 4,we propose a new chaotic system by introducing additional feedback states into the classical lorentz system.We use Lyapunov index and dimension to analyze the system,and give the phase diagram of the system for verification,so as to study the dynamic behavior of the system.The results show that the system is chaotic in a wide range and exhibits many properties,such as stability,period,chaos,quasiorbital period,etc.In chapter 5,we construct a new chaotic system by introducing additional feedback state and adding constant multiplier to the cross product term.We find that the system has only one equilibrium point,but it can evolve into periodic,quasi-periodic,chaotic and hyperchaotic dynamic states.It is found that the system has positive lyapunov index in the parameter range.Therefore,the system has good properties and wide application prospects.Chapter 6 summarizes the main work involved in this paper and prospects the research direction.