恒元物理学讲座（第062期）：Complex and multilayer networks: from structure to dynamics

讲座内容：Coupled biological and chemical systems, neural networks, social interacting species, the Internet and the World Wide Web, are only a few examples of systems composed by a huge number of highly interconnected units. The first approach to capture the global properties of such systems is to model them as graphs whose nodes represent the constituent units, and whose links stand for the interactions between them. On the one hand, scientists have to cope with structural issues, such as characterizing the topology of a complex wiring architecture, revealing the unifying principles that are at the basis of real networks, and developing models to mimic the growth of a network and reproduce its structural properties. On the other hand, many relevant questions arise when studying complex networks’ dynamics, such as learning how large ensembles of dynamical systems that interact through a complex wiring topology can behave collectively. Furthermore, interactions in real-world networks cannot be treated on an equivalent footing, as they may have a time-varying, or a context-related multilayer nature. In my talk, I will try to overview the major concepts and results recently achieved in the study of the structure and dynamics of complex networks, and summarize some relevant, novel, applications of these ideas indifferent disciplines, such as nonlinear science, social science, biology, statistical mechanics, medicine and engineering.

In particular, I will point to the existence of three distinct classes of networked systems: physical, functional and parenclitic networks, whose consequences and applications will be summarized.