Bifurcation Research Of Two Kinds Of Delayed Computer Virus Models

With the continuous innovation and development of science and technology,computers play an indispensable role in the development of human society and bring earth-shaking changes to human life.At the same time,the types and quantities of computer viruses are also increasing rapidly,which has brought huge economic losses to society.Therefore,effective prevention,control and detection of the spread of computer viruses is an urgent and arduous task in the development of today's society.Nowadays,the research on the bifurcation and control of delay computer virus model has attracted much attention of many scholars.Due to the hysteresis of virus transmission among computers,the research of computer viruses will be more abundant,complex dynamic behavior and close to the actual background of computer viruses transmission.Therefore,the research on Hopf bifurcation and Bogdanov-Takens bifurcation of delay computer viruses model will help to further study the spread of computer viruses and provide better strategies to prevent and effectively control the spread of viruses.It will also further broaden the related fields of computer virus research.This thesis studies Hopf bifurcation and Bogdanov-Takens bifurcation of two types of computer viruses with delay.The main contents and innovations of the full text are summarized as follows(1)To study a class of two delays computer virus model with latent nodes that is likely to be infected with viruses.The delays of the model are reflected in that it takes a certain period of time for the infected node to reinstall the system and the antivirus software to clear the latent nodes.This paper discusses the bifurcations of the system with two delays taking the same value.Firstly,by analyzing the characteristic equations of the virus-free equilibrium point and the positive virus equilibrium point,the sufficient conditions for the system to generate Hopf bifurcation and the existence of a cluster of periodic solutions at the positive virus equilibrium point are given Secondly,using delay as the bifurcation parameter,the center manifold theorem and the canonical theorem are applied to calculate the bifurcation direction and stability conditions of the periodic solution of Hopf bifurcation When the delay passes through the critical value,the system generates Hopf bifurcation and periodic solutions near the positive equilibrium point.Finally,through the MATLAB numerical simulation,the time history diagram and phase diagram of the system are obtained,which verifies the correctness of the theoretical results(2)Study a class of delay computer virus models with nonlinear incidence,and the Hopf bifurcation and Bogdanov-Takens bifurcation of the model are analyzed.The Bogdanov-Takens bifurcation is first proposed in the study of delay computer virus models.Firstly,with the delay as the bifurcation parameter,the sufficient conditions for the Hopf bifurcation of the system are given,and the direction of the Hopf bifurcation and the stability of the periodic solution are obtained.Secondly,the distribution of the characteristic roots of the linear part at the positive equilibrium point is analyzed,and the critical condition for the codimensional 2 bifurcation of the system is obtained.Finally,using the center manifold theorem and the canonical theorem,the second-order canonical form of the system on the center manifold is calculated.