On dynamics of xs quadratic stochastic operators - Mukhamedov, Farrukh; Saburov, Mansoor; Mohd Jamal, Afifah Hanum (World Science Publishing Company, 2012)
In this research we introduce a new class of quadratic stochastic operators called xs-QSO which are defined through coefficient of the operator from measure-theoretic (namely we are looking the coefficient as the measures which are absolute continuous or singular) point of view. We also study the limiting behaviour of xs -QSO defined on 2D-simplex. We first describe xi-s -QSO on 2Dsimplex and classify them with respect to the conjugacy and renumeration of the coordinates. We find six non-isomorphic classes of such operators. Moreover, we investigate the behaviour of each operator from three classes and prove convergence of trajectories of these classes and study their certain properties. We showed trajectories of two classes converge to the equilibrium. For the third class, it is established only the negative trajectories converge to the equilibrium.