Effects Of Knowledge Limitation On Network Construction And Network Dynamics

The structure and dynamical behaviors of complex networks operating have attracted much attention in recent years. There are various networks in the world around us. One of the reasons of studying networks is to find out common topological features shared by the real-world networks and attempt to reveal the basic mechanisms underlying these common features. The other reason is to investigate the effects of the topological features on the network dynamical behaviors.The study of complex networks shows the possible applications in various fields. For instance, the structure of optical communication networks can be designed properly so as to improve the speed, efficiency and security of communication, reducing information congestion as far as possible. The couplings and coupling-induced synchronization between optical subsystems is necessary for optical communication. The study of complex networks can provide theoretical support to the optimization of synchronization within large-size fiber-optic communication networks. In this way, the efficiency of optical communication can be improved on one hand., and consumption of energy can be reduced on the other hand. In other fields, for instrance, from the theoretical analysis of networks, one can find an efficient way to inhibit the spreading of virus among people. Since parkinsonism arises from excessive synchronous behaviors among parts of neurons, one can find a method towards successful treatment of parkinsonism from the network study. Therefore, the investigations of complex networks are important in various fields.The main work in this paper is to study the effects of the knowledge limitation on the scale-free network construction, on the network traffics and on the network synchronization behavior.(1) We study the effect of knowledge limitation on the network construction. We propose a modification of scale-free BA model. In the modified model, new nodes can only link to a part of already existing nodes according to the geographic limitation of the knowledge of news nodes. The preferential attachment rule is applied but only to a connected subset rather than the whole networks. The numerical results show that the constructed networks are scale-free networks. From the study of the dependence of the heterogeneity on the knowledge limitation, it is found that the construction probability and the degree distribution of the network follow super-linear preferential attachment rule. The origin of scale-free network under super-linear preferential attachment rule is explained and the slight adjustment of network heterogeneity is proposed.(2) We investigate the effects of the knowledge limitation on the traffic flows within networks. We propose a load-dependent random walks network model. In this model, the loads of nodes at this time step influence the walks at the next time step. The knowledge limitation considered here includes two aspects. Firstly, the information available to walkers is limited to connection conditions of only neighboring nodes of the node that the walker is currently at. Secondly, the information is limited to loads at the previous time step while the information at the earlier steps is inevitable or ignored. Thus the considered walks of the network are preferential. We compare the load distribution between non-preferential and preferential walks. It is found that loads are redistributed and linearly dependent on node degrees for non-preference walks. While they are linearly dependent on high-order degrees and eventually tend to eigenvector centrailities for preferential walks. Comparison of homogeneous and heterogeneous networks shows that heterogeneous scale-free networks are more sensitive to walk preference. We find that large-degree nodes are protected from overload failures. We study the cascading failures triggered by load-redistribution-induced overload failures and discuss the effects of the degree correlation. The possible method of reducing the cascading failures is proposed.(3) We study the effects of knowledge limitation on network synchronizability. The network coupling strengths are weighted according to"local loads"of nodes. The numerical calculations of several networks show that the network synchronizability is optimized when coupling weighting procedure is based on softly limited information. The synchronization phenomenon is not so good for both global (unlimited) information and extremely limited information. This is in contrast with the expectation that more information always favor the enhancement of network synchronizability. We find that the result is true for both complete synchronization of identical oscillators and phase synchronization of nonidentical oscillators. The main result does not depend on the degree of heterogeneous and the size of the network. From the distribution of weighted nodes in the network, suitable local load can enhance the synchronization. We provide a method to estimate the network synchronizability without calculating eigenvalues of coupling matrix.The results of this paper show that the structure and the dynamical behavior of the network will vary under knowledge limitation.