572 research outputs found
Dynamical Systems on Networks: A Tutorial
We give a tutorial for the study of dynamical systems on networks. We focus
especially on "simple" situations that are tractable analytically, because they
can be very insightful and provide useful springboards for the study of more
complicated scenarios. We briefly motivate why examining dynamical systems on
networks is interesting and important, and we then give several fascinating
examples and discuss some theoretical results. We also briefly discuss
dynamical systems on dynamical (i.e., time-dependent) networks, overview
software implementations, and give an outlook on the field.Comment: 39 pages, 1 figure, submitted, more examples and discussion than
original version, some reorganization and also more pointers to interesting
direction
Multilayer Networks
In most natural and engineered systems, a set of entities interact with each
other in complicated patterns that can encompass multiple types of
relationships, change in time, and include other types of complications. Such
systems include multiple subsystems and layers of connectivity, and it is
important to take such "multilayer" features into account to try to improve our
understanding of complex systems. Consequently, it is necessary to generalize
"traditional" network theory by developing (and validating) a framework and
associated tools to study multilayer systems in a comprehensive fashion. The
origins of such efforts date back several decades and arose in multiple
disciplines, and now the study of multilayer networks has become one of the
most important directions in network science. In this paper, we discuss the
history of multilayer networks (and related concepts) and review the exploding
body of work on such networks. To unify the disparate terminology in the large
body of recent work, we discuss a general framework for multilayer networks,
construct a dictionary of terminology to relate the numerous existing concepts
to each other, and provide a thorough discussion that compares, contrasts, and
translates between related notions such as multilayer networks, multiplex
networks, interdependent networks, networks of networks, and many others. We
also survey and discuss existing data sets that can be represented as
multilayer networks. We review attempts to generalize single-layer-network
diagnostics to multilayer networks. We also discuss the rapidly expanding
research on multilayer-network models and notions like community structure,
connected components, tensor decompositions, and various types of dynamical
processes on multilayer networks. We conclude with a summary and an outlook.Comment: Working paper; 59 pages, 8 figure
Data based identification and prediction of nonlinear and complex dynamical systems
We thank Dr. R. Yang (formerly at ASU), Dr. R.-Q. Su (formerly at ASU), and Mr. Zhesi Shen for their contributions to a number of original papers on which this Review is partly based. This work was supported by ARO under Grant No. W911NF-14-1-0504. W.-X. Wang was also supported by NSFC under Grants No. 61573064 and No. 61074116, as well as by the Fundamental Research Funds for the Central Universities, Beijing Nova Programme.Peer reviewedPostprin
The structure and dynamics of multilayer networks
In the past years, network theory has successfully characterized the
interaction among the constituents of a variety of complex systems, ranging
from biological to technological, and social systems. However, up until
recently, attention was almost exclusively given to networks in which all
components were treated on equivalent footing, while neglecting all the extra
information about the temporal- or context-related properties of the
interactions under study. Only in the last years, taking advantage of the
enhanced resolution in real data sets, network scientists have directed their
interest to the multiplex character of real-world systems, and explicitly
considered the time-varying and multilayer nature of networks. We offer here a
comprehensive review on both structural and dynamical organization of graphs
made of diverse relationships (layers) between its constituents, and cover
several relevant issues, from a full redefinition of the basic structural
measures, to understanding how the multilayer nature of the network affects
processes and dynamics.Comment: In Press, Accepted Manuscript, Physics Reports 201
Dynamic processes on networks and higher-order structures
Higher-order interactions are increasingly recognized as a critical aspect in the modeling of complex systems. Higher-order networks provide a framework for studying the relationship between the structure of higher-order interactions and the function of the complex system. However, little is known about how higher-order interactions affect dynamic processes. In this thesis, we develop general frameworks of percolation aiming at understanding the interplay between higher-order network structures and the critical properties of dynamics. We reveal that degree correlations strongly affect the percolation threshold on higher-order networks and interestingly, the effect of correlations is different on ordinary percolation and higher-order percolation. We further elucidate the mechanisms responsible for the emergence of discontinuous transitions on higher-order networks. Moreover, we show that triadic regulatory interaction, as a general type of higher-order interaction found widely in nature, can turn percolation into a fully-fledged dynamic process that exhibits period doubling and a route to chaos. As an important example of dynamic processes, we further investigate the role of network topology on epidemic spreading. We show that higher-order interactions can induce a non-linear infection kernel in a pandemic, which results in a discontinuous phase transition, hysteresis, and superexponential spreading. Finally, we propose an epidemic model to evaluate the role of automated contact-and-tracing with mobile apps as a new containment measure to mitigate a pandemic. We reveal the non-linear effect on the reduction of the incidence provided by a certain fraction of app adoption in the population and we propose the optimal strategy to mitigate the pandemic with limited resources. Altogether, the thesis provides new insights into the interplay between the topology of higher-order networks and their dynamics. The results obtained may shed light on the research in other areas of interest such as brain functions and epidemic spreading
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