The Dynamics Of A Computer Virus Propagation Model With Double Delays

Since21st century, computer network system has grown stronger and strongerwith the fast development of information technology. More and more applicationsbased on computer networks have come into our daily life and affected us, thusmaking computer networks an essential tool in our daily life. However, computersare also faced with the virus invasion when bring us more convenience. Virus hasbecome a major threat to computers. Now people use the anti-virus technology toidentify the characteristics of the computer virus. But this technology usually makework after the time when new virus "break" in computers. So we can see that it’svery significant for controlling the computer virus by mastering the breaking way ofcomputer virus.In this paper, we study a kind of computer virus model with double delays.Firstly, we introduce some background information and current situation of thecomputer virus model.Secondly, analyze the existence of the equilibriums and discuss the twoequilibriums of the model: the virus-free equilibrium and the virus equilibrium.i)analyze the virus-free equilibrium. Ways are as following: first, make a delayparameter20and chose1as parameter, analyze the stability of the virus-freeequilibrium;Second, when the delay parameter1is in the stability region, wemake2as parameter, then we analyze the stability of the virus-free equilibrium.ii) we analyze the stability of the virus equilibrium using the above similarmethod and the conditions of existence for Hopf bifurcation.Using the centermanifold theory and normal form method to get Hopf bifurcation’s direction and thespecific calculation formula of the stability of periodic solution.Finally, we make some numerical simulation with Matlab,so that the conclusionof this paper is verified.