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On the orthogonality preserving quadratic stochastic operators

Mukhamedov, Farrukh and Mohd. Taha, Mohd. Hafizuddin (2015) On the orthogonality preserving quadratic stochastic operators. AIP Conference Proceedings , 1660. 050057-1 -050057-8. ISSN 0094-243X (P), 1551-7616 (O)

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A quadratic stochastic operator (in short QSO) is usually used to present the time evolution of differing species in biology. Some quadratic stochastic operators have been studied by Lotka and Volterra. In the present paper, we first give a simple characterization of Volterra QSO in terms of absolutely continuity of discrete measures. Further, we introduce a notion of orthogonal preserving QSO, and describe such kind of operators defined on two dimensional simplex. It turns out that orthogonal preserving QSOs are permutations of Volterra QSO. The associativity of genetic algebras generated by orthogonal preserving QSO is studied too.

Item Type: Article (Journal)
Additional Information: 5537/42973 International Conference on Mathematics, Engineering and Industrial Applications 2014 (ICoMEIA 2014)
Uncontrolled Keywords: Quadratic stochastic operator; Volterra operator; orthogonal preserving
Subjects: Q Science > QA Mathematics
Kulliyyahs/Centres/Divisions/Institutes (Can select more than one option. Press CONTROL button): Kulliyyah of Science > Department of Computational and Theoretical Sciences
Depositing User: Dr. Farrukh Mukhamedov
Date Deposited: 05 Jun 2015 15:51
Last Modified: 05 Jun 2015 15:51
URI: http://irep.iium.edu.my/id/eprint/42973

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