Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Dynamic social network models incorporating stochasticity and delays


Authors: H. T. Banks, Keri Rehm and Karyn L. Sutton
Journal: Quart. Appl. Math. 68 (2010), 783-802
MSC (2000): Primary 91D30, 91C20, 34F05, 34K50
Published electronically: September 23, 2010
MathSciNet review: 2761244
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Abstract: Networks are typically studied via computational models, and often investigations are restricted to the static case. Here we extend the work in Banks, Karr, Nguyen and Samuels (2008), which demonstrated a simple dynamical system framework in which to study social network behavior, to include a discrete delay. This delay represents the time lag that is likely required for an agent to change his/her own characteristics (e.g., opinions, viewpoints or behavior) after interacting with an agent possessing different characteristics. Thus this modification adds significantly to the relevance of the model in many potential applications. We have shown that the delays can be incorporated into a stochastic differential equations (SDE) framework in an efficient and computationally tractable way. Through numerical studies, we see novel outcomes when stochasticity, delay, or both are considered, demonstrating the need to include these features should they be present in the network application.


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Additional Information

H. T. Banks
Affiliation: Center for Research in Scientific Computation, Center for Quantitative Studies in Biomedicine, North Carolina State University, Raleigh, North Carolina 27695-8212

Keri Rehm
Affiliation: Center for Research in Scientific Computation, Center for Quantitative Studies in Biomedicine, North Carolina State University, Raleigh, North Carolina 27695-8212

Karyn L. Sutton
Affiliation: Center for Research in Scientific Computation, Center for Quantitative Studies in Biomedicine, North Carolina State University, Raleigh, North Carolina 27695-8212

DOI: https://doi.org/10.1090/S0033-569X-2010-01201-X
Keywords: Social networks, stochastic differential equations, delay differential equations, clustering
Received by editor(s): July 18, 2009
Published electronically: September 23, 2010
Article copyright: © Copyright 2010 Brown University
The copyright for this article reverts to public domain 28 years after publication.


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