On uniqueness of fixed points of positive quadratic stochastic operators
We know from the theory of Markov chains that any positive square stochastic matrix has a unique fixed point in the simplex and its trajectory starting from any initial point of the simplex converges to that unique fixed point. However, in general, the similar result for a positive cubic stochastic...
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| Format: | Conference or Workshop Item |
| Language: | English |
| Published: |
2015
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| Subjects: | |
| Online Access: | http://irep.iium.edu.my/46251/ http://irep.iium.edu.my/46251/ http://irep.iium.edu.my/46251/4/ID46251.pdf |
| Summary: | We know from the theory of Markov chains that any positive square stochastic matrix has a unique fixed point in the simplex and its trajectory starting from any initial point of the simplex converges to that unique fixed point. However, in general, the similar result for a positive cubic stochastic matrix does not hold true. We know that a cubic stochastic matrix is associated with a quadratic stochastic operator defined on the simplex. In this paper, we provide a uniqueness criterion for fixed points of positive quadratic stochastic operators defined on 2D simplex. |
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