Hopf Bifurcation And Control Of Complex Network Model With Multiple Delays

In recent years,the complex networks has attracted much attention and set off a research boom at home and abroad.Its stability and bifurcation problems are the focus of research in dynamic systems.The study of complex networks can help us find some common phenomena and characteristics of artificial networks and nature,and translate theoretical results into practical applications,so as to further understand the real world.Among them,the disease spreading network model is a dynamic model that reflects the actual situation of virus spreading.Studying the dynamic performance of the model has important practical significance for the prevention and control measures and the immune strategy.The essence of neural network model is to use computer language to simulate the decision-making process of human brain.Studying this model has important guiding significance for exploring the laws of human brain thinking and intelligent activities,and designing learning algorithms to solve practical problems based on the research results.This paper mainly studies the dynamic behavior and bifurcation control of these two kinds of network models.1.The Hopf bifurcation problem of a disease spreading network model under parameter control is studied.Firstly,the influence of parameters p on bifurcation of system is investigated,and the conditions for bifurcation generation and the stability interval of the model are obtained.Then,we discuss the bifurcating properties of the system with μ as a bifurcation parameter.Finally,the direction and stability of the bifurcating periodic solution are discussed in detail,and the expressions of three important parameters that determine the properties of the bifurcating periodic solution are derived.Simulation examples show that adjusting the system parameters can achieve ideal dynamic behavior.2.The bifurcation behavior of a neural network with mixed delays is studied.The original system is transformed into the two-neuron system by introducing a virtual neuron,and a hybrid controller is designed for the system to study stability and bifurcation of the controlled system.Moreover,the properties of the bifurcating periodic solution are obtained using center manifold and normal form theory.Finally,numerical simulation is used to verify the results of theoretical analysis,and the hybrid control method and time-delay feedback control method are compared.3.The stability and Hopf bifurcation of fractional complex valued neural networks(FCVNNs)with two leakage delays are studied.Two time delays are respectively selected as bifurcation parameters to describe the dynamic properties of FCVNNs,and the conditions of the equilibrium point is asymptotic stability and system undergoes Hopf bifurcation are obtained,and the conclusions are verified by numerical simulation.In addition,the simulation shows that adjusting the fractional order of FCVNNs can make the bifurcation occur in advance or delay.4.The bifurcation control problem of ternary fractional complex neural network with leakage delay and discrete delay is studied.The bifurcation behavior of the system is adjusted by changing the feedback gain parameters of the feedback controller,and the theoretical bifurcation results are further verified by the bifurcation diagram.In addition,simulation examples are used to demonstrate the influence of feedback gain parameters on system stability and limit cycle amplitude,revealing the relationship between fractional order and critical values of bifurcation parameters.