Dynamical Systems on Networks: A Tutorial

Abstract

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.

39 pages, 1 figure, submitted, more examples and discussion than original version, some reorganization and also more pointers to interesting directions

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Cited by in corpus (51)

• The physics of higher-order interactions in complex systems
• The physics of spreading processes in multilayer networks
• Unification of theoretical approaches for epidemic spreading on complex networks
• Mathematical frameworks for oscillatory network dynamics in neuroscience
• Topological data analysis of contagion maps for examining spreading processes on networks
• Persistent homology of time-dependent functional networks constructed from coupled time series
• Coupled Dynamics on Hypergraphs: Master Stability of Steady States and Synchronization
• Kinetics of Social Contagion
• A message-passing approach for recurrent-state epidemic models on networks
• Spectra of networks containing short loops
• Estimating inter-event time distributions from finite observation periods in communication networks
• Spectra of random networks with arbitrary degrees
• Temporal profiles of avalanches on networks
• Topological data analysis of continuum percolation with disks
• Network cloning unfolds the effect of clustering on dynamical processes
• Complex active optical networks as a new laser concept
• Hipsters on Networks: How a Small Group of Individuals Can Lead to an Anti-Establishment Majority
• Spatial Applications of Topological Data Analysis: Cities, Snowflakes, Random Structures, and Spiders Spinning Under the Influence
• Clusters and the entropy in opinion dynamics on complex networks
• Contagion on complex networks with persuasion
• Impact of temporal network structures on the speed of consensus formation in opinion dynamics
• What are essential concepts about networks?
• Asynchronous Networks and Event Driven Dynamics
• Message-Passing Methods for Complex Contagions
• Fitting In and Breaking Up: A Nonlinear Version of Coevolving Voter Models
• Opinion dynamics on tie-decay networks
• Correlated Cascades: Compete or Cooperate
• On the reliable and efficient numerical integration of the Kuramoto model and related dynamical systems on graphs
• A Phase Model with Large Time Delayed Coupling
• Self-segregation in heterogeneous metapopulation landscapes
• Rejection-Based Simulation of Non-Markovian Agents on Complex Networks
• Detection of Functional Communities in Networks of Randomly Coupled Oscillators Using the Dynamic-Mode Decomposition
• A random walker's view of networks whose growth it shapes
• Spatial Strength Centrality and the Effect of Spatial Embeddings on Network Architecture
• Electronic implementation of a dynamical network with nearly identical hybrid nodes via unstable dissipative systems
• Multivariate Spatiotemporal Hawkes Processes and Network Reconstruction
• Recovering the Graph Underlying Networked Dynamical Systems under Partial Observability: A Deep Learning Approach
• Chaotic fluctuations in graphs with amplification
• The K Shortest Paths Problem with Application to Routing
• Influence Prediction for Continuous-Time Information Propagation on Networks
• Low-dimensional controllability of brain networks
• Topological data analysis of truncated contagion maps
• Contact Process with Exogenous Infection and the Scaled SIS Process
• Modeling random walkers on growing random networks
• Network Inference from Population-Level Observation of Epidemics
• Nonlinear Modal Decoupling of Multi-Oscillator Systems with Applications to Power Systems
• Adaptive Diffusion Processes of Time-Varying Local Information on Networks
• Dynamics of social contagions with local trend imitation
• Synergistic effects in threshold models on networks
• Diffusion in Networks and the Unexpected Virtue of Burstiness
• Persistent Threshold Dynamics with Recovery in Complex Networks