2016/05/30 by Augusto Santos, Santos, Augusto Almeida, Soummya Kar +5
Computer Science · Decision Sciences · Physics and Astronomy · #FOS: Physical sciences #Game Theory and Applications #Neural Networks Stability and Synchronization #Opinion Dynamics and Social Influence #Physics and Society (physics.soc-ph)
paper · pdf · doi:10.48550/arxiv.1605.09450
openalex publication_date 2016/05/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We propose a family of models to study the evolution of ties in a network of interacting agents by reinforcement and penalization of their connections according to certain local laws of interaction. The family of stochastic dynamical systems, on the edges of a graph, exhibits good convergence properties, in particular, we prove a strong-stability result: a subset of binary matrices or graphs -- characterized by certain compatibility properties -- is a global almost sure attractor of the family of stochastic dynamical systems. To illustrate finer properties of the corresponding strong attractor, we present some simulation results that capture, e.g., the conspicuous phenomenon of emergence and downfall of leaders in social networks.