Study On Dynamical Processes Of Propagation And Coupling Over Complex Networks

Complex network modeling has been considered as an important interdiscipline approach for describing and understanding complex systems.Because of universality and diversity of its research objects,it has attracted broad attentions of researchers in many fields all over the world.Complex networks are ubiquitous around our lives, ranging from nature to human socity.Any complex network system can be viewed as a graph of interacted individuals,where nodes denote individuals and links denote interactions between them.The well-known and extensively studied networks include Internet,World Wide Web,railway networks,airport networks,the power grid,proteinprotein interaction networks,metabolic networks,gene regulatory networks,neuron networks,human relationship networks,etc.Extensive researches of these networks in the past a few years have completely changed the traditional view about the real world networks and spurred the rapid development of the interdisciplinary scientific fields.Complex network modeling approach focus on macroscopical phenomena result from the interactions of individuals.Apart from traditional reductionism usually used by physicists,by complex network modeling approach point of view,the investigating system is seen as a whole,the interactions of individuals inside the system are focused on and rich overall behaviors of the system are predicted including self-organised properties, emergence and other phenomena.So far,the investigation of complex networks has covered many fields,including mathmatics,physics,chemistry,biology,technology and social sciences.The ultimate goal of studying complex networks is to understand how topological properties affect the dynamical processes taking place on them.Researches on information propagation and coupling phenomena over complex networks are of the greatest importance.There are many papers concerning propagation dynamics and synchronization over complex networks in the literature,including epidemic spreading, information propagation,game,synchronization and so on.Inspired by the current international research interests,we focused on the information propagation dynamics and synchronization phenomena over the complex networks.The works we do in these fields are following:We have systematically investigated the dynamics of information propagation over scale-free networks.Because the sizes of modern communication networks are becoming bigger and bigger,even worse,the topology of the networks is everchanging,the traditional routing strategies,which based on the global topological information,suffer lack of storage and computational power.Considering this situation,we have proposed several routing strategies of sending data packets only based on local information.We can quantify the capacity of a network by the phase transition from free flow state to congestion state,and we have found the optimal parameter values,resulting in the highest efficiency of scale-free networks.Moreover,we found appropriately increasing information of network topology can greatly increase the capacity of the network,for example,next nearest-neighbor searching strategy.In the practical design of the routing strategy,we can trade off cost against capability of the system in order to find an optimal solution.Our results may be useful for designing next generation routing protocol.We have studied the collective synchronization behavior over scale-free networks and proposed a decoupling process to enhance the synchronizability of scale-free networks. With perturbation on the network structure,we investigated how th characteristic parameters,for example the average shortest path,the maximum betweenness and so on,affect the synchronizability of the networks.We find that the maximum betweenness have a linear-like relation with synchronizability of the network.The results indicate that the maximum betweenness is a best token of network synchronizability among similar network structure so far.We also investigated geographical effect on small-world network synchronization. Many real world networks are embeded in some specific space,nodes have coordinets and links denote some real interactions.We have explored the effects of coupling strength, which coming from geographical restriction,on network synchronizability on one- and two- dimensional lattices.It is found that network synchronizability is a nontrivial function of distance and coupling strength.Our findings shed some light on the collective dynamics of real coupled systems.We find information propagation on a complex network have some relations with synchronization on the network:Networks with high system capacity often show high network synchronizability.Actually,synchronization process is also a process of transmission of coupling information.The two seemingly irrelevant research subjects have the same underlying dynamical nature,reflecting different aspects of the properties of the system.