Research On Hopf Bifurcation And Periodic Impulsive Feedback Control For Two Classes Of Fractional Order Differential Equation Models With Delay

Since fractional-order differential equations with delay are more suitable for charac-terizing the evolutionary process with time delay and memory,they have been extensively applied to various fields such as biology,elasticity,neural networks,physics,material science and control theory.In particular,due to its higher accuracy in describing and sim-ulating the evolution of biological systems,the research of fractional-order differential equations with delay has important application value for revealing the laws of population dynamics.In addition,fractional-order differential equations with delay can be also used to construct genetic neural network systems,its research is helpful to provide theoretical support for the study of machine learning algorithms.This thesis is concerned with Hopf bifurcations,periodic pulse feedback control and anti-control of chaos for two classes of fractional-order differential equation models with delay by the linearized theory of differential equations and numerical simulation methods.The main research contents and results of this thesis are as follows:1.A class of fractional-order delay predator-prey model incorporating a prey refuge is studied:(?).Firstly,the existence and uniqueness of the solution of the initial value problem for the model is proved by using the Banach fixed point theorem.Secondly,taking time delay as the bifurcation parameter,Hopf bifurcation of the model is studied by using the bifurca-tion theory,and a novel periodic pulse delay feedback controller is designed to effectively control Hopf bifurcation for the proposed model.Finally,the predictor-corrector scheme is used to perform numerical simulations to verify the theoretical analysis results.2.A class of fractional-order simplified five-neuron BAM neural network models with double delays is studied:(?).Firstly,the linearized system of this model is studied,and some conditions are given for the existence of pure imaginary roots of its characteristic equation.Secondly,taking time delay as the bifurcation parameter,Hopf bifurcation of the model is studied by using the bifurcation theory.A novel piecewise periodic pulse delay feedback controller is designed to effectively control the delay-deduced Hopf bifurcation of the model.The anti-control of chaos for this model is also studied by using chaos theory and 0-1 test for chaos.Finally,the predictor-corrector scheme is used to perform numerical simulations to verify the theoretical analysis results.The research results of this thesis on Hopf bifurcation control of the fractional-order delay predator-prey model provide a scientific evidence for selecting economic and effec-tive control strategies in ecological management.The research results on the anti-control of chaos for the fractional-order simplified five-neuron BAM neural network models with double delays provide a novel technique for constructing chaotic neural network systems.