On dynamics of xs quadratic stochastic operators

Mukhamedov, Farrukh and Saburov, Mansoor and Mohd Jamal, Afifah Hanum (2012) On dynamics of xs quadratic stochastic operators. International Journal of Modern Physics: Conference Series, 9 (1). pp. 299-307. ISSN 2010-1945

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Abstract

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.

Item Type:	Article (Journal)
Additional Information:	5537/23710
Uncontrolled Keywords:	Quadratic stochastic operator; trajectory; dynamics
Subjects:	Q Science > QA Mathematics
Kulliyyahs/Centres/Divisions/Institutes (Can select more than one option. Press CONTROL button):	Kulliyyah of Science > Department of Computational and Theoretical Sciences
Depositing User:	Dr. Farrukh Mukhamedov
Date Deposited:	12 Jun 2012 08:58
Last Modified:	28 Dec 2012 14:28
URI:	http://irep.iium.edu.my/id/eprint/23710

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