A Class Of Random Network Attack And Dynamic System Model And Its Threshold Properties

The structure of computer networks in the real world is very similar to the topo-logical property of complex networks, so the discussion of defense dynamical system in complex networks is very popular recently. The establishment of cyber defense dynam-ical system is generally based on the modified SIS model with a series of conclusions about the threshold, mostly the threshold is represented by an expression of spreading capability and defense capability, especially the ratio of them. In this paper, we main-ly construct a more generalized cyber defense dynamics based on the SIS model, and make the threshold do not depend on the parameters in the model, but determined by the type of dynamics we have constructed, the initial state of the nodes and the topology of networks.This paper includes five parts, the first part briefly introduces the constructions of complex networks as well as the mainly outcomes of the related papers in recent years. The second part constructs the attack-defense dynamics model in complex networks, and defines four types of "defense intensity function" which are mainly discussed in this paper. The third part draws the conclusions about the threshold of the dynamical system constructed by different types of "defense intensity function" in the condition of degree independent initial occupation. The fourth part firstly defines the expected de-gree sequence, and gives the specific method for the generation of complex networks. On this basis, this part will also give the conclusions about the threshold in the condi-tion of degree dependent initial occupation, and apply the results to the estimation of threshold for the power-law random network. The fifth part firstly constructs complex networks of five different types by the method of numerical simulation, and then sim-ulates the conclusions about threshold for different assumptions of the initial states of nodes as well as for the dynamical systems constructed by different types of "defense intensity function"...