Evolutionary Dynamics Of Complex Networks And Dynamical Processes Over Complex Networks

Complex network modeling has been considered as an important approach for describing and understanding complex systems. A complex system is composed of many interacted individuals, which can be naturally represented by a graph with individuals denoted by nodes and interactions by links. From this point of view, complex networks are ubiquitous, ranging from nature to society. In the past few years, we have witnessed a great devotion of scientists to understanding the underlying mechanisms of complex networks together with the dynamical processes taking place on them. The advances of complex networks are propelled by several parallel developments, including the computerization of data acquisition, increase of computing power, breakdown of boundaries between disciplines and increasing needs for understanding the behavior of an integrated complex system as a whole. Since the groundwork laid by Barabasi, Albert, Watts and strogatz, more and more attention has been given to this emerging field. The widely observed "small-world" and "scale-free" properties shared by many real networks have now completely changed the traditional view and even knowledge of many people on the real-world networks and spurred the rapid development of the interdisciplinary scientific field.So far, the investigation of complex networks has covered many fields, including physics, chemistry, technology and biology, where intensively studied networks cover as diverse as the Internet, World Wide Web, point-to-point networks, collaboration networks, airport networks, power grids, protein-protein interaction networks, genetic regulatory networks and epidemic spreading networks, etc. These networks are of high technological and intellectual importance and the desire to understand such interwoven complex systems has encountered significant challenges as well. The ultimate goal of studying complex networks is to understand how topological properties affect the dynamical processes taking place on them. However, what should be first done is to deeply understand how complex networks possess those common topological features in a self-organized way. Inspired by the current international research interests, we focused on the evolutionary dynamics of the network structures and the dynamical processes occurring over complex networks. Our work contains the evolution of weighted networks, information traffics on scale-free networks, synchronization on networks, evolutionary games on networks, Boolean dynamics and genetic regulatory networks.We have proposed several evolutionary models for weighted networks, including the traffic driven model, the mutual selection model and the mutual attraction model. The weighted networks generated by such models possess power-law distributions of strengths, weights and degrees with the exponents tuned by model parameters between 2—3, which are well consistent with the empirical evidence. In particular, the weighted network generated by the traffic driven model has a disassortative mixing property and a nonlinear correlation between strength and degree, which are in good agreement with real weighted technological networks. For the mutual selection model, the obtained statistical hierarchical property by the model can well reproduce the real observations about weighted social networks. The mutual attraction model can generate networks with both assorta-tive and disassortative mixing properties, indicating that the model can well mimic social networks, technological networks and biological networks. Especially, our work has provided a good answer to one of the ten leading questions in the study of complex networks: why all social networks are assortative, while technological and biological networks are disassortative?We have systematically investigated the dynamics of information traffics over scale-free networks. Several routing strategies of managing data packets have been proposed, including the local routing strategy and the mixed routing strategy based on local static and dynamic 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 of each model, resulting in the highest efficiency of scale-free networked traffic systems. Moreover, we have found hysteresis loop in networked traffic systems with a finite packet-delivering ability. Such hysteresis loop indicates the existence of bistable states in the traffic dynamics over scale-free networks.We have studied the collective synchronization behavior over scale-free networks and proposed a decoupling process to enhance the synchronizability of scale-free networks. Because of the low cost in performing this task, the decoupling process method may have very good potential applications. Furthermore, we have investigated the epidemic spreading over scale-free networks with community structures and found their synchronization behavior. Interestingly, there exist phase transitions of the synchronizability depending on the strengths of the community structures in the networks. On the basis of the finite size scaling, we have obtained the values of phase transition exponents, indicating that the phase transitions belong to the mean-field type.We have systematically studied the evolutionary games on networks. A memory-based snowdrift game has been proposed. We found that in regular lattices, the cooperation level versus payoff parameter shows a step structure with each step corresponding to a typical spatial pattern. There is a sharp pattern transition between any two different patterns. This interesting phenomenon has not been reported previously. For scale-free networks, the cooperation level versus payoff parameter in the memory-based snowdrift game displays non-monotonous behavior with cooperation level peaking at some specific parameter values, which suggests that suitable encouragement of selfish behavior can lead to the optimal cooperation level.Whereafter, we proposed an evolutionary model by coupling the evolution of games and the network. It is found that the cooperative behavior can be considerably promoted and the scale-free as well as assortative mixing topological properties can emerge from the coevolution. Furthermore, we have presented a preferential learning mechanism and investigated the evolutionary games on weighted adaptive networks for better mimicking the widely observed cooperation behavior. Besides, by adopting the homogenous small-world networks, we have explored the effect of randomness in evolutionary games and found coherence resonance phenomena therein.In order to understand the dynamical properties in the chaotic range of scale-free Boolean networks, we proposed a dynamical coarse graining method performed in the state space. It is found that the weighted and directed state graph possesses five power-law distributions, independent of the strength of the coarse graining. Furthermore, we have explored the dynamics of real genetic regulatory networks of cells by using the Boolean network model. Interestingly, a universal core modular is found. Subsequently, we can classify the cellular regulatory networks under different conditions in terms of the dynamical properties of the core modular. Through the study of the Derrida curve under different conditions, we found that the normal cell is closer to the edge of chaos, which supports the hypothesis of Kauffman.