Nonlinear Mapping Convergence and Application to Social Networks
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arXiv
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| Format: | Preprint |
| Published: |
2017
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| _version_ | 1866929556849426432 |
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| author | Anderson, Brian D. O. Ye, Mengbin |
| author_facet | Anderson, Brian D. O. Ye, Mengbin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1709_08840 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | Nonlinear Mapping Convergence and Application to Social Networks Anderson, Brian D. O. Ye, Mengbin Systems and Control Social and Information Networks General Topology 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. |
| title | Nonlinear Mapping Convergence and Application to Social Networks |
| topic | Systems and Control Social and Information Networks General Topology |
| url | https://arxiv.org/abs/1709.08840 |