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Mukhamedov, Farrukh; Saburov, Mansoor; Qaralleh, Izzat

On \(\xi^{(s)}\)-quadratic stochastic operators on two-dimensional simplex and their behavior. (English) Zbl 1470.47031

Abstr. Appl. Anal. 2013, Article ID 942038, 12 p. (2013).
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. The general problem in the nonlinear operator theory is to study the behavior of operators. This problem was not fully finished even for quadratic stochastic operators which are the simplest nonlinear operators. To study this problem, several classes of QSO were investigated. We study \(\xi^{(s)}\)-QSO defined on 2D simplex. We first classify \(\xi^{(s)}\)-QSO into 20 nonconjugate classes. Further, we investigate the dynamics of three classes of such operators.

Cited in 7 Documents

MSC:

47D07 Markov semigroups and applications to diffusion processes
92D25 Population dynamics (general)
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\textit{F. Mukhamedov} et al., Abstr. Appl. Anal. 2013, Article ID 942038, 12 p. (2013; Zbl 1470.47031)
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