Examples of Dynamical Systems

Myriad dynamical systems have been studied in numerous disciplines and from multiple perspectives, and an increasingly large number of these systems have also been examined on networks.

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[35]  Petter Holme,et al.  Modern temporal network theory: a colloquium , 2015, The European Physical Journal B.

[36]  S. Redner,et al.  Voter models on heterogeneous networks. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[37]  N. Christakis,et al.  The Spread of Obesity in a Large Social Network Over 32 Years , 2007, The New England journal of medicine.

[38]  George J. Pappas,et al.  Stable flocking of mobile agents part I: dynamic topology , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[39]  Rick Durrett,et al.  Some features of the spread of epidemics and information on a random graph , 2010, Proceedings of the National Academy of Sciences.

[40]  Martin Feinberg,et al.  Multiple Equilibria in Complex Chemical Reaction Networks: I. the Injectivity Property * , 2006 .

[41]  Mathieu Génois,et al.  Temporal Gillespie Algorithm: Fast Simulation of Contagion Processes on Time-Varying Networks , 2015, PLoS Comput. Biol..

[42]  Jie Lin,et al.  Coordination of groups of mobile autonomous agents using nearest neighbor rules , 2003, IEEE Trans. Autom. Control..

[43]  Mason A Porter,et al.  Noise-induced synchronization, desynchronization, and clustering in globally coupled nonidentical oscillators. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

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[45]  T. Valente.  Social network thresholds in the diffusion of innovations , 1996 .

[46]  Mason A. Porter,et al.  Multi-Stage Complex Contagions , 2011, Chaos.

[47]  Arun Sundararajan,et al.  Distinguishing influence-based contagion from homophily-driven diffusion in dynamic networks , 2009, Proceedings of the National Academy of Sciences.

[48]  Jean-Charles Delvenne,et al.  Random Walks, Markov Processes and the Multiscale Modular Organization of Complex Networks , 2014, IEEE Transactions on Network Science and Engineering.

[49]  Derek Ruths,et al.  Control Profiles of Complex Networks , 2014, Science.

[50]  Yuni Iwamasa,et al.  Networks maximising the consensus time of voter models , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[51]  Laurent Hébert-Dufresne,et al.  Pathogen mutation modeled by competition between site and bond percolation. , 2013, Physical review letters.

[52]  Andrea Montanari,et al.  The spread of innovations in social networks , 2010, Proceedings of the National Academy of Sciences.

[53]  Yamir Moreno,et al.  Determinants of Meme Popularity , 2015, ArXiv.

[54]  James P. Gleeson,et al.  On Watts' cascade model with random link weights , 2012, J. Complex Networks.

[55]  Mason A. Porter,et al.  Multilayer networks , 2013, J. Complex Networks.

[56]  Piet Van Mieghem,et al.  Epidemic processes in complex networks , 2014, ArXiv.

[57]  Martin Feinberg,et al.  Multiple Equilibria in Complex Chemical Reaction Networks: Ii. the Species-reactions Graph , 2022 .

[58]  S. N. Dorogovtsev,et al.  Bootstrap percolation on complex networks. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[59]  Vito Latora,et al.  Interplay between consensus and coherence in a model of interacting opinions , 2015, ArXiv.

[60]  D. Watts,et al.  A generalized model of social and biological contagion. , 2005, Journal of theoretical biology.

[61]  Peter Sheridan Dodds,et al.  Limited imitation contagion on random networks: chaos, universality, and unpredictability. , 2012, Physical review letters.

[62]  George J. Pappas,et al.  Stable flocking of mobile agents, part I: fixed topology , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[63]  Oliver Riordan,et al.  Explosive Percolation Is Continuous , 2011, Science.

[64]  Jürgen Kurths,et al.  Synchronization - A Universal Concept in Nonlinear Sciences , 2001, Cambridge Nonlinear Science Series.

[65]  A. Pikovsky,et al.  Synchronization: Theory and Application , 2003 .

[66]  Nicolas Brunel,et al.  Fast Global Oscillations in Networks of Integrate-and-Fire Neurons with Low Firing Rates , 1999, Neural Computation.

[67]  Alessandro Vespignani,et al.  Modeling the Worldwide Spread of Pandemic Influenza: Baseline Case and Containment Interventions , 2007, PLoS medicine.

[68]  Mason A. Porter,et al.  Think Locally, Act Locally: The Detection of Small, Medium-Sized, and Large Communities in Large Networks , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[69]  P DeLellis,et al.  Synchronization and control of complex networks via contraction, adaptation and evolution , 2010, IEEE Circuits and Systems Magazine.

[70]  C. Gilligan,et al.  Synergy in spreading processes: from exploitative to explorative foraging strategies. , 2011, Physical review letters.

[71]  E. Ott,et al.  The effect of network topology on the stability of discrete state models of genetic control , 2009, Proceedings of the National Academy of Sciences.

[72]  Michael Small,et al.  Basin of attraction determines hysteresis in explosive synchronization. , 2014, Physical review letters.

[73]  Ling-Yun Wu,et al.  Structure and dynamics of core/periphery networks , 2013, J. Complex Networks.

[74]  Takuya Machida,et al.  Turing instability in reaction–diffusion models on complex networks , 2014, 1405.0642.

[75]  Ming Tang,et al.  Dynamics of social contagions with memory of non-redundant information , 2015, Physical review. E, Statistical, nonlinear, and soft matter physics.

[76]  Paul L. Krapivsky,et al.  Reinforcement-driven spread of innovations and fads , 2011, ArXiv.

[77]  Alex Arenas,et al.  Synchronization reveals topological scales in complex networks. , 2006, Physical review letters.

[78]  Gergely Röst,et al.  Generalization of Pairwise Models to non-Markovian Epidemics on Networks. , 2015, Physical review letters.

[79]  Yamir Moreno,et al.  Cascading behaviour in complex socio-technical networks , 2013, J. Complex Networks.

[80]  Michael Aizenman,et al.  Metastability effects in bootstrap percolation , 1988 .

[81]  Denis Mollison,et al.  Spatial Contact Models for Ecological and Epidemic Spread , 1977 .

[82]  Noah E. Friedkin.  Social Influence Network Theory , 2006 .

[83]  Andrew Mellor,et al.  Role of Luddism on Innovation Diffusion , 2015, Physical review. E, Statistical, nonlinear, and soft matter physics.

[84]  Virgil D. Gligor,et al.  Analysis of complex contagions in random multiplex networks , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[85]  Jari Saramäki,et al.  Temporal Networks , 2011, Encyclopedia of Social Network Analysis and Mining.

[86]  Mingzhou Ding,et al.  Enhancement of neural synchrony by time delay. , 2004, Physical review letters.

[87]  J. Sethna.  Statistical Mechanics: Entropy, Order Parameters, and Complexity , 2021 .

[88]  T. Ichinomiya.  Frequency synchronization in a random oscillator network. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[89]  Thomas W. Valente.  Network models of the diffusion of innovations , 1996, Comput. Math. Organ. Theory.

[90]  Filippo Menczer,et al.  Virality Prediction and Community Structure in Social Networks , 2013, Scientific Reports.

[91]  Francesco Bullo,et al.  Opinion Dynamics and the Evolution of Social Power in Influence Networks , 2015, SIAM Rev..

[92]  Christian T. Brownlees,et al.  Bank credit risk networks: Evidence from the Eurozone , 2020 .

[93]  S. Fortunato,et al.  Statistical physics of social dynamics , 2007, 0710.3256.

[94]  Russell Lyons,et al.  The Spread of Evidence-Poor Medicine via Flawed Social-Network Analysis , 2010, 1007.2876.

[95]  Mason A. Porter,et al.  A mathematical model for the dynamics and synchronization of cows , 2010, 1005.1381.

[96]  Thomas House,et al.  Exact and approximate moment closures for non-Markovian network epidemics. , 2015, Journal of theoretical biology.

[97]  David Terman,et al.  Mathematical foundations of neuroscience , 2010 .

[98]  D. Parisi,et al.  Comparison of voter and Glauber ordering dynamics on networks. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[99]  S. Strogatz.  From Kuramoto to Crawford: exploring the onset of synchronization in populations of coupled oscillators , 2000 .

[100]  J. Spencer,et al.  Explosive Percolation in Random Networks , 2009, Science.

[101]  Matthew O. Jackson,et al.  Diffusion and Contagion in Networks with Heterogeneous Agents and Homophily , 2011 .

[102]  Yoshiki Kuramoto,et al.  Chemical Oscillations, Waves, and Turbulence , 1984, Springer Series in Synergetics.

[103]  Luc Moreau,et al.  Stability of multiagent systems with time-dependent communication links , 2005, IEEE Transactions on Automatic Control.

[104]  M. Macy,et al.  Complex Contagions and the Weakness of Long Ties1 , 2007, American Journal of Sociology.

[105]  P. Leath,et al.  Bootstrap percolation on a Bethe lattice , 1979 .

[106]  P. Trapman,et al.  On analytical approaches to epidemics on networks. , 2007, Theoretical population biology.

[107]  V. Jansen,et al.  Modelling the influence of human behaviour on the spread of infectious diseases: a review , 2010, Journal of The Royal Society Interface.

[108]  Mason A. Porter,et al.  Communities in Networks , 2009, ArXiv.

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[110]  S. Redner,et al.  Constrained opinion dynamics: freezing and slow evolution , 2003 .

[111]  Thomas K. D. M. Peron,et al.  The Kuramoto model in complex networks , 2015, 1511.07139.

[112]  Gerardo Iñiguez,et al.  Local cascades induced global contagion: How heterogeneous thresholds, exogenous effects, and unconcerned behaviour govern online adoption spreading , 2016, Scientific Reports.

[113]  Cosma Rohilla Shalizi,et al.  Homophily and Contagion Are Generically Confounded in Observational Social Network Studies , 2010, Sociological methods & research.

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[119]  Albert-László Barabási,et al.  Control Principles of Complex Networks , 2015, ArXiv.

[120]  Albert-László Barabási,et al.  Controllability of complex networks , 2011, Nature.

[121]  R. Spigler,et al.  The Kuramoto model: A simple paradigm for synchronization phenomena , 2005 .

[122]  Petter Holme,et al.  Threshold model of cascades in temporal networks , 2012, ArXiv.

[123]  Madalena Chaves,et al.  Robustness and fragility of Boolean models for genetic regulatory networks. , 2005, Journal of theoretical biology.

[124]  A. Jadbabaie,et al.  On the stability of the Kuramoto model of coupled nonlinear oscillators , 2005, Proceedings of the 2004 American Control Conference.

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[126]  David F. Gleich,et al.  PageRank beyond the Web , 2014, SIAM Rev..

[127]  F. Caccioli,et al.  Stability analysis of financial contagion due to overlapping portfolios , 2014 .

[128]  T. Vicsek,et al.  Uncovering the overlapping community structure of complex networks in nature and society , 2005, Nature.

[129]  Stephen Coombes,et al.  Mathematical Frameworks for Oscillatory Network Dynamics in Neuroscience , 2015, The Journal of Mathematical Neuroscience.

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[132]  Mark E. J. Newman,et al.  The small-world effect is a modern phenomenon , 2013, ArXiv.

[133]  S. Redner,et al.  Voter model on heterogeneous graphs. , 2004, Physical review letters.

[134]  Ali Jadbabaie.  Flocking in Networked Systems , 2015, Encyclopedia of Systems and Control.

[135]  Z. Wang,et al.  The structure and dynamics of multilayer networks , 2014, Physics Reports.

[136]  E. Schöll,et al.  Heterogeneous delays in neural networks , 2013, 1311.1919.

[137]  Noah J. Cowan,et al.  Nodal Dynamics, Not Degree Distributions, Determine the Structural Controllability of Complex Networks , 2011, PloS one.

[138]  Piet Van Mieghem,et al.  Exact Markovian SIR and SIS epidemics on networks and an upper bound for the epidemic threshold , 2014, 1402.1731.

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[144]  George J. Pappas,et al.  Analysis and Control of Epidemics: A Survey of Spreading Processes on Complex Networks , 2015, IEEE Control Systems.

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[146]  V. Eguíluz,et al.  Conservation laws for the voter model in complex networks , 2004, cond-mat/0408101.

[147]  Dylan Walker,et al.  Tie Strength, Embeddedness, and Social Influence: A Large-Scale Networked Experiment , 2014, Manag. Sci..

[148]  James P. Gleeson,et al.  Competition-induced criticality in a model of meme popularity , 2013, Physical review letters.

[149]  G. Whitham,et al.  Linear and Nonlinear Waves , 1976 .

[150]  Mason A. Porter,et al.  Eigenvector-Based Centrality Measures for Temporal Networks , 2015, Multiscale Model. Simul..

[151]  Alessandro Vespignani,et al.  Reaction–diffusion processes and metapopulation models in heterogeneous networks , 2007, cond-mat/0703129.

[152]  Duncan J Watts,et al.  A simple model of global cascades on random networks , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[153]  Timoteo Carletti,et al.  Turing patterns in multiplex networks. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[154]  Maxi San Miguel,et al.  Is the Voter Model a model for voters? , 2013, Physical review letters.

[155]  S. Scarpino,et al.  The effect of a prudent adaptive behaviour on disease transmission , 2016, Nature Physics.

[156]  Alessandro Vespignani,et al.  influenza A(H1N1): a Monte Carlo likelihood analysis based on , 2009 .

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[159]  Duccio Fanelli,et al.  Multiple-scale theory of topology-driven patterns on directed networks. , 2015, Physical review. E.

[160]  Lars Backstrom,et al.  Structural diversity in social contagion , 2012, Proceedings of the National Academy of Sciences.

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[165]  Kristina Lerman,et al.  The "Majority Illusion" in Social Networks , 2015, PloS one.

[166]  Naoki Masuda,et al.  A Gillespie Algorithm for Non-Markovian Stochastic Processes , 2016, SIAM Rev..

[167]  Reuven Cohen,et al.  Limited path percolation in complex networks. , 2007, Physical review letters.

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[170]  J. Robins,et al.  Second look at the spread of epidemics on networks. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[171]  S. Redner,et al.  Dynamics of vacillating voters , 2007, 0710.0914.

[172]  Sergey N. Dorogovtsev,et al.  K-core Organization of Complex Networks , 2005, Physical review letters.

[173]  Lada A. Adamic,et al.  The Diffusion of Support in an Online Social Movement: Evidence from the Adoption of Equal-Sign Profile Pictures , 2015, CSCW.

[174]  Adilson E Motter,et al.  Network synchronization landscape reveals compensatory structures, quantization, and the positive effect of negative interactions , 2009, Proceedings of the National Academy of Sciences.

[175]  J. Gómez-Gardeñes,et al.  From scale-free to Erdos-Rényi networks. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[176]  Raissa M. D'Souza,et al.  Anomalous critical and supercritical phenomena in explosive percolation , 2015, Nature Physics.

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[178]  Matteo Magnani,et al.  Spreading Processes in Multilayer Networks , 2014, IEEE Transactions on Network Science and Engineering.

[179]  Hans J. Herrmann,et al.  Shock waves on complex networks , 2014, Scientific Reports.

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[181]  Reza Olfati-Saber,et al.  Flocking for multi-agent dynamic systems: algorithms and theory , 2006, IEEE Transactions on Automatic Control.

[182]  Martin Rosvall,et al.  Effect of Memory on the Dynamics of Random Walks on Networks , 2014, J. Complex Networks.