Bifurcation,Chaos And Control Of Complex Networks

In recent years,the upsurge of complex network research is in the ascendant,especially on the study of bifurcation and stability of complex networks.The study of its bifurcation and stability can provide theoretical guidance for our life and production.However,after research,it is found that system's movement and its properties may not be within our expectation,finding a way to change the system's motion by adding controls to the original system to change the critical value of the system's bifurcation and produce the result to meet our needs.For complex systems,there is also a more widely used theory that is the phenomenon of mixing.The application of chaos phenomena is very broad,involving fields such as communications,cryptography,weather and aerospace.In the first chapters,the related knowledge and development profile of bifurcation,complex network,chaos and so on are briefly introduced,and the theoretical knowledge involved in the research process is briefly introduced,and the main work contents involved in this article are also discussed.In the third chapter,we add a delay feedback control to a ring complex network with n neurons.The ring network is very common in our life,and some people have carried out the n-ring network with time delay After deep research,this article intends to add a controller to the ring network without delay and study the stability and bifurcation characteristics of the network by using the delay in the controller as a variable parameter to find out the critical value,the stability of the bifurcation direction and periodic solution of the system provide theoretical guidance for our life and production.In the fourth chapter,we consider a time-delay network system with five neurons.This system has many kinds of connectivity is closely to our real life.Based on the theory of normal type and central manifold theorem,choose bifurcation parameters to discuss the stability,bifurcation behavior of the system and the stability of the periodic solution.With the constant time delay,the system will have a very significantchange in the movement behavior.Finally,the numerical simulation is carried out to verify the conclusion.In the fifth chapter,first we introduces the classical Lorentz system,and gives the relevant properties of the Lorentz system.Based on this,we add two new controllers and obtain a new nonlinear system,which preserves the initial When the initial values ??of the system are different,the system's motion behavior is different.Given a specific parameter value,the system is proved to be a chaos by Lyapunov exponents,dimensions and time series System,and simulates the chaotic attractor.It is discussed that when different values ??of certain parameters are different,the system will have different motion behaviors such as chaos and period.The sixth chapter,summarizes the main research work of this paper,and prospects the future research direction.