DYNAMICAL COMPLEXITY OF NONLINEAR NETWORKS
Zhigang Zheng · Progress in physics · 2009
This review article tries to systematically summarize and review important progreses in dynamical complexity of nonlinear networks,which is a key project supported by the NSFC. The theory,demonstration and application of complex networks have innovativeness and distinguished features. Three monographs and more than 120 SCI and 15 EI articles are published. Characteristics of complexity and quantitative features of complex networks are revealed profoundly. A unified hybrid network theoretical frame is set up,including three theoretical models and a network complexity pyramid. Another family of complex network——generalized Farey tree network——and its organized pyramid are introduced. It is found that transition relations exist between complexity-simplicity and diversity-universality. The relationship between topological properties and dynamical behaviours is revealed. Partial (generalized) synchronization in reguler network models with a few shoutcuts is investigated and partial synchronization criterion is proposed,which is further applied to synchronize spatiotemporal systems with sparse connections. Several models,methods and ways for improving synchronizability are proposed,which are associated with topological characteristic quantitaties,optimal synchronization,synchronization prefirential,various weights and influence of leaf nodes. Multi-objective control strategies in different subnetworks for chaotic connected networks are suggested. Synchronization and control of beam halo-chaos in beam transport network with small-world (BTN-SW) and bean transport network with scale-free (BTN-SF) are realized by new methods. Adaptive velocity model for swarm aggregation is proposed,which provides a powerful mechanism in biological and technological multiagent systems. The traffic-routing control and gaming of resource competition on the Internet are researched. Some spreading laws on different kinds of networks are explored. The evolution features of weighted economic scientist cooperation network are studied. High-tech networks with 4 levels and large online social networks are investigated. Furthermore,a non-equilibrium statistical method is suggested,and macroscopic network is promoted toward microscopic networks(quantum information and nano inference networks). In the past 4 years,we have organized and attended a number of academic conferences at home and abroad. 38 graduate students and PhD students graduated.