Classification ofξ^(s)-Quadratic Stochastic Operators on 2D simplex

Classification of a new subclass of ξ(as)-QSO and its dynamics

“…If ξ 2 is the trivial, i.e., ξ 2 = {∆ m }, then we call the corresponding QSO by ξ (a) -QSO (where the "a" stands for absolute continuous), since in this case every two vectors P ii and P jj are equivalent. We note that some classes of ξ (as) -QSO have been studied in [13,16,17]. In the present paper, we investigate the classification and dynamics of a subclass of ξ (a) .…”

“…We note that in [13], it has been investigated ξ (a) -QSO related to the partition ξ 1 which is the maximal partition of P 3 and in the paper [17] it has been studied ξ (s) -QSO related to the partitions ξ 2 , ξ 3 , ξ 4 .…”

“…We notice that in [13] it has been studied ξ a) -QSO related to the partition ξ 1 . In this paper we will study the subclass of ξ (a) -QSO related to the partitions ξ 2 , ξ 3 , ξ 4 .…”

“…Therefore, many classes of QSO have not been studied. Recently, a new class of QSO called ξ (as) was introduced [12][13][14]17]. This class is defined by some partition of the coupled index set P m = {(i, j) : i < j} ⊂ I × I, where I is a set of integer numbers.…”

“…The dynamics of ξ (as) -QSO that correspond to the point partition (the maximal partition) of P 3 have been investigated in [12,17]. In [13,16] it has been studied some class of ξ (as) -QSO. In this paper, we investigate another new subclass of ξ (as) -QSO and classify them into 18 non-conjugate classes.…”