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An Advanced Persistent Distributed Denial-of-Service Attacked Dynamical Model on Networks

The advanced persistent distributed denial-of-service (APDDoS) attack does a serious harm to cyber security. Establishing a mathematical model to accurately predict APDDoS attack on networks is still an important problem that needs to be solved. Therefore, to help us understand the attack mechanisms of APDDoS on networks, this paper first puts forward a novel dynamical model of APDDoS attack on networks. A systematic analysis of this new model shows that the maximum eigenvalue of the networks is a vital factor that determines the success or failure of the attack. What is more, a new sufficient condition for the global stability of attack-free equilibrium is obtained. The global attractivity of attacked equilibrium has also been proved. Eventually, this paper gives some numerical simulations to show the main results.