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Complex networks: Topology, dynamics and synchronization. (English) Zbl 1044.37561
Summary: Dramatic advances in the field of complex networks have been witnessed in the past few years. This paper reviews some important results in this direction of rapidly evolving research, with emphasis on the relationship between the dynamics and the topology of complex networks. Basic quantities and typical examples of various complex networks are described; and main network models are introduced, including regular, random, small-world and scale-free models. The robustness of connectivity and the epidemic dynamics in complex networks are also evaluated. To that end, synchronization in various dynamical networks are discussed according to their regular, small-world and scale-free connections.
MSC:
37N99Applications of dynamical systems
94C05Analytic circuit theory
37B15Cellular automata
92B20General theory of neural networks (mathematical biology)
68T05Learning and adaptive systems