2014/01/21 by Noah E. Friedkin, Friedkin, Noah E.
Computer Science · Physics and Astronomy · #FOS: Computer and information sciences #FOS: Mathematics #Multiagent Systems (cs.MA) #Neural Networks Stability and Synchronization #Nonlinear Dynamics and Pattern Formation #Opinion Dynamics and Social Influence #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.1401.5339
openalex publication_date 2014/01/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A simple object (one point in m-dimensional space) is the resultant of the evolving matrix polynomial of walks in the irreducible aperiodic network structure of the first order DeGroot (weighted averaging) state-space process. This paper draws on a second order generalization the DeGroot model that allows complex object resultants, i.e, multiple points with distinct coordinates, in the convex hull of the initial state-space. It is shown that, holding network structure constant, a unique solution exists for the particular initial space that is a sufficient condition for the convergence of the process to a specified complex object. In addition, it is shown that, holding network structure constant, a solution exists for dampening values sufficient for the convergence of the process to a specified complex object. These dampening values, which modify the values of the walks in the network, control the system's outcomes, and any strongly connected typology is a sufficient condition of such control.