Application Of Chaos Theory To The Researches On Complex Networks

In the nature and society,complex networks exist everywhere,such as Internet,WWW, biological network,transports network and communication network.For this kind of realistic condition,much attention has been attracted.In this article,we apply the theory of chaos and statistical mechanism to deeply study damage to complex networks by means of MC simulation.In this article,the study of damage to complex networks mainly focuses on the method of attack which means to cut off all links between the removal node and other nodes in complex networks.However,the studies ahead are mostly based on a complete knowledge about the network topology.Here,we propose a method which applies the theory of chaos to take effective attack without any prior information of the network topology.By comparison with ideal intentional attack in scale-free network,we find that our method is very effective.There are mainly three parts in the article.First,we discuss some fundamental concepts in complex networks,such as degree and degree distribution,average shortest path and clustering coefficient.After that,we propose what the criterion is in different networks, random network,small-world network and scale-free network for example.These network models provide important basic theory for studies.Then,we deeply discuss one aspect of dynamical complex networks and that is damage to complex networks.There are two kinds of damage,one is attack and the other is cascade breakdown.And the two parameters which can be used to estimate the damage are average shortest path and the relative size of the largest sub-network.Last,in scale-free network,the following three attacks are considered and compared,(1) random attack,the nodes are randomly selected and removed;(2) ideal intentional attack,the nodes with the largest degree are selected and removed;(3) our method attack,the nodes found by our method are selected and removed.After MC simulation,we find that even without any prior information of the network topology,our method is very effective and robust against disturbs.