Stability And Hopf Bifurcation Of A Computer Virus Model With Time Delays And Virus Mutation

In this paper,a two-delay computer virus propagation dynamics model with virus mutation characteristics is established and studied.Using differential equa-tion qualitative and stability theory and time delay differential equation theory,two types of virus mutation delays to computer viruses are studied the impact of communication.This article is divided into five parts.The first chapter introduces the research background and development status of computer virus models.In the second chapter,establish a class of double-delay computer virus prop-agation dynamics model with virus mutation characteristics,discuss the positive and bounded solutions of the computer virus system,and calculate the existence conditions of the virus-free equilibrium point,the boundary equilibrium point and the coexistence equilibrium point of the two viruses;using the characteristic root method to obtain the local stability condition of the virus-free equilibrium point,by constructing the Lyapunov function and LaSalle's invariance principle,the global asymptotic stability of the virus-free equilibrium point of the model is analyzed;when ?2=0,use the Routh-Hurwitz criterion to analyze the local asymptotic sta-bility of the boundary equilibrium point E1*of the model;using the same method,when ?1=0,analyze the local asymptotic stability of the boundary equilibrium point E2*of the model;when ?1=0.?2=0 analyze the local asymptotic stability of the point of the model where two viruses coexist.In the third chapter,the conditions of Hopf bifurcation near the coexistence equilibrium point of the two viruses E*is studied in various situations,and then the paradigm method and the central manifold theorem are used to discuss the current when ?2=0 or ?1=0,and for any ?1,?2,the bifurcation direction of the Hopf bifurcation and the stability of the periodic solution.In the fourth chapter,numerical simulations are performed by the Matlab,and the validity of the theoretical results are verified.From the numerical simulation,it can be seen that the change of two mutation delays will affect the coexistence form of two kinds of viruses in the computer network.When the two delays are small enough(less than the corresponding critical values),the two viruses will eventually tend to a stable level.With the increase of the delay,the stability of the coexistence equilibrium point of the two viruses E*will disappear,and with the occurrence of bifurcation phenomenon of the system,system(2.1)will have periodic oscillation,and the number of two types of computer viruses will show periodic change.In the fifth chapter,summarize the main research content of this article as well as the methods adopted and conclusions drawn.