Ordering dynamics and aging in the Symmetrical Threshold model

The so-called Granovetter-Watts model was introduced to capture a situation in which the adoption of new ideas or technologies requires a certain redundancy in the social environment of each agent to take effect. This model has become a paradigm for complex contagion. Here we investigate a symmetric version of the model: agents may be in two states that can spread equally through the system via complex contagion. We find three possible phases: a mixed one (dynamically active disordered state), an ordered one, and a heterogeneous frozen phase. These phases exist for several configurations of the contact network. Then we consider the effect of introducing aging as a non-Markovian mechanism in the model, where agents become increasingly resistant to change their state the longer they remain in it. We show that when aging is present, the mixed phase is replaced, for sparse networks, by a new phase with different dynamical properties. This new phase is characterized by an initial disordering stage followed by a slow ordering process towards a fully ordered absorbing state. In the ordered phase, aging modifies the dynamical properties. For random contact networks, we develop a theoretical description based on an Approximate Master Equation that describes with good accuracy the results of numerical simulations for the model with and without aging.

[1]  Byungjoon Min,et al.  Threshold Cascade Dynamics in Coevolving Networks , 2023, Entropy.

[2]  Bradley Dirks,et al.  The minimal exponent and k-rationality for local complete intersections , 2022, Journal de l’École polytechnique — Mathématiques.

[3]  J. Ramasco,et al.  Aging in binary-state models: The Threshold model for complex contagion. , 2022, Physical review. E.

[4]  J. Ramasco,et al.  Aging effects in Schelling segregation model , 2022, Scientific Reports.

[5]  M. San Miguel,et al.  Echo chambers and information transmission biases in homophilic and heterophilic networks , 2022, Scientific Reports.

[6]  G. Bianconi,et al.  Non-Markovian majority-vote model. , 2020, Physical review. E.

[7]  B. Nowak,et al.  Symmetrical threshold model with independence on random graphs. , 2020, Physical review. E.

[8]  Raúl Toral,et al.  Reduction from non-Markovian to Markovian dynamics: the case of aging in the noisy-voter model , 2019, Journal of Statistical Mechanics: Theory and Experiment.

[9]  Y. Moreno,et al.  Social contagion models on hypergraphs , 2019, Physical Review Research.

[10]  Yu Xu,et al.  How behavior spreads: the science of complex contagions , 2019, Information, Communication & Society.

[11]  F. Toschi,et al.  Interevent time distributions of avalanche dynamics , 2019, 1906.09897.

[12]  Raul Toral,et al.  Ordering dynamics in the voter model with aging , 2019, Physica A: Statistical Mechanics and its Applications.

[13]  Bartlomiej Nowak,et al.  Homogeneous Symmetrical Threshold Model with Nonconformity: Independence versus Anticonformity , 2019, Complex..

[14]  S. Redner,et al.  Reality-inspired voter models: A mini-review , 2018, Comptes Rendus Physique.

[15]  Maxi San Miguel,et al.  Aging-induced continuous phase transition , 2018, Physical Review E.

[16]  M San Miguel,et al.  Analytical and numerical study of the non-linear noisy voter model on complex networks. , 2018, Chaos.

[17]  Maxi San Miguel,et al.  Fragmentation transitions in a coevolving nonlinear voter model , 2017, Scientific Reports.

[18]  Arkadiusz Jędrzejewski,et al.  Pair approximation for the q-voter model with independence on complex networks. , 2016, Physical review. E.

[19]  Gian Paolo Rossi,et al.  Walls-in-one: usage and temporal patterns in a social media aggregator , 2016, Applied Network Science.

[20]  Maxi San Miguel,et al.  Dynamics on networks: competition of temporal and topological correlations , 2016, Scientific Reports.

[21]  Andrew Mellor,et al.  Characterization of the nonequilibrium steady state of a heterogeneous nonlinear q-voter model with zealotry , 2016, ArXiv.

[22]  V. Eguíluz,et al.  Competition in the presence of aging: dominance, coexistence, and alternation between states , 2015, Scientific Reports.

[23]  Mauro Mobilia,et al.  Nonlinear $q$-voter model with inflexible zealots , 2015, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[25]  Raúl Toral,et al.  Simulating non-Markovian stochastic processes. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[27]  J. Gleeson.  Binary-state dynamics on complex networks: pair approximation and beyond , 2012, 1209.2983.

[28]  James P. Gleeson,et al.  Cascades on clique-based graphs , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[29]  S. Havlin,et al.  Communication activity in a social network: relation between long-term correlations and inter-event clustering , 2012, Scientific Reports.

[30]  J. Gleeson.  High-accuracy approximation of binary-state dynamics on networks. , 2011, Physical review letters.

[31]  V. Eguíluz,et al.  Update rules and interevent time distributions: slow ordering versus no ordering in the voter model. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[32]  James P. Gleeson,et al.  Cascades on a class of clustered random networks , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[33]  Jari Saramäki,et al.  Small But Slow World: How Network Topology and Burstiness Slow Down Spreading , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[34]  V. I. Bykov,et al.  Dynamics of first-order phase transitions , 2009 .

[35]  Esteban Moro,et al.  Impact of human activity patterns on the dynamics of information diffusion. , 2009, Physical review letters.

[36]  James P Gleeson,et al.  Cascades on correlated and modular random networks. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[37]  F. Schweitzer,et al.  Decelerating microdynamics can accelerate macrodynamics in the voter model. , 2007, Physical review letters.

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

[39]  J. Gleeson,et al.  Seed size strongly affects cascades on random networks. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[40]  Spain,et al.  Cascade dynamics of multiplex propagation , 2005, physics/0504165.

[41]  V. Eguíluz,et al.  Voter model dynamics in complex networks: Role of dimensionality, disorder, and degree distribution. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[43]  F. Moreira,et al.  Majority-vote model on random graphs. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[44]  F. Moreira,et al.  Small-world effects in the majority-vote model. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[45]  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.

[46]  T. Liggett,et al.  Stochastic Interacting Systems: Contact, Voter and Exclusion Processes , 1999 .

[47]  B. Derrida.  HOW TO EXTRACT INFORMATION FROM SIMULATIONS OF COARSENING AT FINITE TEMPERATURE , 1997 .

[48]  P. Krapivsky,et al.  Coarsening and persistence in the voter model. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[49]  Hakim,et al.  Exact first-passage exponents of 1D domain growth: Relation to a reaction-diffusion model. , 1995, Physical review letters.

[50]  Bernard Derrida,et al.  EXPONENTS APPEARING IN THE ZERO-TEMPERATURE DYNAMICS OF THE 1D POTTS MODEL , 1995 .

[51]  Dietrich Stauffer,et al.  Universality at the three-dimensional percolation threshold , 1994 .

[52]  Mark S. Granovetter.  Threshold Models of Collective Behavior , 1978, American Journal of Sociology.

[53]  R. Toral,et al.  Binary-state dynamics on complex networks: Stochastic pair approximation and beyond , 2020 .

[54]  W. Marsden.  I and J , 2012 .

[55]  N. Wormald.  Models of random regular graphs , 2010 .

[56]  L. Haan,et al.  Extreme value theory : an introduction , 2006 .

[57]  M. J. Oliveira,et al.  Isotropic majority-vote model on a square lattice , 1992 .

[58]  P. Erdos,et al.  On the evolution of random graphs , 1984 .