Nonlinear Mapping Convergence and Application to Social Networks

Abstract

This paper discusses discrete-time maps of the form $x(k+1)=F(x(k))$, focussing on equilibrium points of such maps. Under some circumstances, Lefschetz fixed-point theory can be used to establish the existence of a single locally attractive equilibrium (which is sometimes globally attractive) when a general property of local attractivity is known for any equilibrium. Problems in social networks often involve such discrete-time systems, and we make an application to one such problem.

Submission to European Control Conference 2018

References in corpus (2)

• Evolution of Social Power in Social Networks with Dynamic Topology
• On the Analysis of the DeGroot-Friedkin Model with Dynamic Relative Interaction Matrices

Cited by in corpus (2)

• Evolution of Social Power in Social Networks with Dynamic Topology
• Applications of the Poincaré--Hopf Theorem: Epidemic Models and Lotka--Volterra Systems