**Volume 17, Issue 4, pp 535-544**

**Publication Date**: 2017-11-01

**Izzat Qaralleh**
- Department of Mathematics, Tafila Technical University, P. O. Box 179. zip code 66110, Tafila, Jordan

A quadratic stochastic operator (QSO) describes the time evolution of different species in biology. The main problem with regard to a nonlinear operator is to study its behavior. This subject has not been studied in depth; even QSOs, which are the simplest nonlinear operators, have not been studied thoroughly. In this paper we introduce a new subclass of \(\xi^{(as)}\)-QSO defined on 2D simplex. first we classify this subclass into 18 non-conjugate classes. Furthermore, we investigate the behavior of one class.

Quadratic stochastic operator, \(\ell\)-Volterra quadratic stochastic operator, \(\xi^{(s)}\)-quadratic stochastic operator, permuted \(\ell\)-Volterra quadratic stochastic operator, dynamics

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