MMN-1090
On volterra and orthogonality preserving quadratic stochaistic operators
Abstract
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.
Vol. 17 (2016), No. 1, pp. 457-470
DOI: 10.18514/MMN.2016.1090