Anderson, BrianYe, Mengbin2020-02-18June 12-159783952426999http://hdl.handle.net/1885/201769This paper discusses nonlinear 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.The work of M. Ye and B.D.O. Anderson was supported by the Australian Research Council (ARC) under grants DP-130103610 and DP-160104500, and by Data61@CSIRO (formerly NICTA Ltd.). M. Ye was supported by an Australian Government Research Training Program (RTP) Scholarship.6 pagesapplication/pdfen-AU© 2018 EUCA. Publisher email reply 2/5/2014 advising can archive accepted version of conference paper.Manifolds, Convergence, Eigenvalues and eigenfunctions, Social network services, Standards, Mathematical model, Jacobian matrices201810.23919/ECC.2018.85501972019-11-25