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Binary-state dynamics on complex networks: pair approximation and beyond

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dc.contributor.author Gleeson, James P.
dc.date.accessioned 2015-04-30T15:15:46Z
dc.date.available 2015-04-30T15:15:46Z
dc.date.issued 2013
dc.identifier.citation Gleeson, JP (2013) 'Binary-State Dynamics on Complex Networks: Pair Approximation and Beyond'. Physical Review X, 3 . en_US
dc.identifier.uri http://hdl.handle.net/10344/4444
dc.description peer-reviewed en_US
dc.description.abstract A wide class of binary-state dynamics on networks-including, for example, the voter model, the Bass diffusion model, and threshold models-can be described in terms of transition rates (spin-flip probabilities) that depend on the number of nearest neighbors in each of the two possible states. High-accuracy approximations for the emergent dynamics of such models on uncorrelated, infinite networks are given by recently developed compartmental models or approximate master equations (AMEs). Pair approximations (PAs) and mean-field theories can be systematically derived from the AME. We show that PA and AME solutions can coincide under certain circumstances, and numerical simulations confirm that PA is highly accurate in these cases. For monotone dynamics (where transitions out of one nodal state are impossible, e.g., susceptible-infected disease spread or Bass diffusion), PA and the AME give identical results for the fraction of nodes in the infected (active) state for all time, provided that the rate of infection depends linearly on the number of infected neighbors. In the more general nonmonotone case, we derive a condition-that proves to be equivalent to a detailed balance condition on the dynamics-for PA and AME solutions to coincide in the limit t -> infinity. This equivalence permits bifurcation analysis, yielding explicit expressions for the critical (ferromagnetic or paramagnetic transition) point of such dynamics, that is closely analogous to the critical temperature of the Ising spin model. Finally, the AME for threshold models of propagation is shown to reduce to just two differential equations and to give excellent agreement with numerical simulations. As part of this work, the Octave or Matlab code for implementing and solving the differential-equation systems is made available for download. en_US
dc.language.iso eng en_US
dc.publisher American Physical Society en_US
dc.relation 317614
dc.relation.ispartofseries Physical Review X;3, 021004
dc.relation.uri http://dx.doi.org/10.1103/PhysRevX.3.021004
dc.subject collective behavior en_US
dc.subject model en_US
dc.subject spread en_US
dc.subject recruitment en_US
dc.subject contagion en_US
dc.subject graphs en_US
dc.title Binary-state dynamics on complex networks: pair approximation and beyond en_US
dc.type info:eu-repo/semantics/article en_US
dc.type.supercollection all_ul_research en_US
dc.type.supercollection ul_published_reviewed en_US
dc.date.updated 2015-04-30T15:03:05Z
dc.description.version PUBLISHED
dc.identifier.doi 10.1103/PhysRevX.3.021004
dc.contributor.sponsor SFI en_US
dc.contributor.sponsor ERC en_US
dc.relation.projectid 11/PI/1026 en_US
dc.relation.projectid 09/SR/E1780 en_US
dc.relation.projectid 317614 en_US
dc.rights.accessrights info:eu-repo/semantics/openAccess en_US
dc.internal.rssid 1441491
dc.internal.copyrightchecked Yes
dc.description.status peer-reviewed


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