On volterra and orthogonality preserving quadratic stochastic operators
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 abso...
| Main Authors: | , |
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| Format: | Article |
| Language: | English English English |
| Published: |
University of Miskolc
2016
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| Subjects: | |
| Online Access: | http://irep.iium.edu.my/50835/ http://irep.iium.edu.my/50835/ http://irep.iium.edu.my/50835/ http://irep.iium.edu.my/50835/1/50835_-_On_volterra_and_orthogonality_preserving_quadratic_stochastic_operators.pdf http://irep.iium.edu.my/50835/4/50835_On%20volterra%20and%20orthogonality%20preserving%20quadratic_wos.pdf http://irep.iium.edu.my/50835/5/50835_On%20volterra%20and%20orthogonality%20preserving%20quadratic_scopus.pdf |
| Summary: | 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. Moreover, we provide its generalization in
continuous setting. 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 |
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