Dynamical phenomena in complex networks: fundamentals and applications
Institute of Mathematics, Technische Universität Berlin, Berlin, Germany
2 Department of Physics, School of Philosophy, Sciences and Letters of Ribeirão Preto, University of São Paulo, 14040-901, Ribeirão Preto, SP, Brazil
3 Federal University of São Paulo, São José dos Campos, SP, Brazil
4 National Institute for Space Research, São José dos Campos, SP, Brazil
5 Earth System Analysis and Complexity Science, Potsdam Institute for Climate Impact Research (PIK), Member of the Leibniz Association, 14473, Potsdam, Germany
6 Institute of Information Technology, Mathematics and Mechanics, Lobachevsky University of Nizhny Novgorod, 603950, Nizhny Novgorod, Russia
This special issue presents a series of 33 contributions in the area of dynamical networks and their applications. Part of the contributions is devoted to theoretical and methodological aspects of dynamical networks, such as collective dynamics of excitable systems, spreading processes, coarsening, synchronization, delayed interactions, and others. A particular focus is placed on applications to neuroscience and Earth science, especially functional climate networks. Among the highlights, various methods for dealing with noise and stochastic processes in neuroscience are presented. A method for constructing weighted networks with arbitrary topologies from a single dynamical node with delayed feedback is introduced. Also, a generalization of the concept of geodesic distances, a path-integral formulation of network-based measures is developed, which provides fundamental insights into the dynamics of disease transmission. The contributions from the Earth science application field substantiate predictive power of climate networks to study challenging Earth processes and phenomena.
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