On quadratic stochastic operators having three fixed points
We knew that a trajectory of a linear stochastic operator associated with a positive square stochastic matrix starting from any initial point from the simplex converges to a unique fixed point. However, in general, the similar result for a quadratic stochastic operator associated with a positive cub...
| Main Authors: | , |
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| Format: | Article |
| Language: | English English |
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Institute of Physics Publishing (UK)
2016
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| Online Access: | http://irep.iium.edu.my/51149/ http://irep.iium.edu.my/51149/3/51149.pdf http://irep.iium.edu.my/51149/4/51149_On_Quadratic_Stochastic_Operators_Having_Three_Fixed_Points_SCOPUS.pdf |
| _version_ | 1848783794790727680 |
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| author | Saburov, Mansoor Yusof, Nur Atikah |
| author_facet | Saburov, Mansoor Yusof, Nur Atikah |
| author_sort | Saburov, Mansoor |
| building | IIUM Repository |
| collection | Online Access |
| description | We knew that a trajectory of a linear stochastic operator associated with a positive square stochastic matrix starting from any initial point from the simplex converges to a unique fixed point. However, in general, the similar result for a quadratic stochastic operator associated with a positive cubic stochastic matrix does not hold true. In this paper, we provide an
example for the quadratic stochastic operator with positive coefficients in which its trajectory
may converge to different fixed points depending on initial points. |
| first_indexed | 2025-11-14T16:27:01Z |
| format | Article |
| id | iium-51149 |
| institution | International Islamic University Malaysia |
| institution_category | Local University |
| language | English English |
| last_indexed | 2025-11-14T16:27:01Z |
| publishDate | 2016 |
| publisher | Institute of Physics Publishing (UK) |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | iium-511492017-01-09T08:11:15Z http://irep.iium.edu.my/51149/ On quadratic stochastic operators having three fixed points Saburov, Mansoor Yusof, Nur Atikah QA Mathematics We knew that a trajectory of a linear stochastic operator associated with a positive square stochastic matrix starting from any initial point from the simplex converges to a unique fixed point. However, in general, the similar result for a quadratic stochastic operator associated with a positive cubic stochastic matrix does not hold true. In this paper, we provide an example for the quadratic stochastic operator with positive coefficients in which its trajectory may converge to different fixed points depending on initial points. Institute of Physics Publishing (UK) 2016-03 Article PeerReviewed application/pdf en http://irep.iium.edu.my/51149/3/51149.pdf application/pdf en http://irep.iium.edu.my/51149/4/51149_On_Quadratic_Stochastic_Operators_Having_Three_Fixed_Points_SCOPUS.pdf Saburov, Mansoor and Yusof, Nur Atikah (2016) On quadratic stochastic operators having three fixed points. Journal of Physics: Conference Series, 697 (1). ISSN 1742-6588 E-ISSN 1742-6596 http://iopscience.iop.org/article/10.1088/1742-6596/697/1/012012/pdf 10.1088/1742-6596/697/1/012012 |
| spellingShingle | QA Mathematics Saburov, Mansoor Yusof, Nur Atikah On quadratic stochastic operators having three fixed points |
| title | On quadratic stochastic operators having three
fixed points |
| title_full | On quadratic stochastic operators having three
fixed points |
| title_fullStr | On quadratic stochastic operators having three
fixed points |
| title_full_unstemmed | On quadratic stochastic operators having three
fixed points |
| title_short | On quadratic stochastic operators having three
fixed points |
| title_sort | on quadratic stochastic operators having three
fixed points |
| topic | QA Mathematics |
| url | http://irep.iium.edu.my/51149/ http://irep.iium.edu.my/51149/ http://irep.iium.edu.my/51149/ http://irep.iium.edu.my/51149/3/51149.pdf http://irep.iium.edu.my/51149/4/51149_On_Quadratic_Stochastic_Operators_Having_Three_Fixed_Points_SCOPUS.pdf |