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On non-ergodic volterra cubic stochastic operators

Mukhamedov, Farrukh and Pah, Chin Hee and Rosli, Azizi (2019) On non-ergodic volterra cubic stochastic operators. Qualitative Theory of Dynamical Systems. ISSN 1575-5460 E-ISSN 1662-3592 (In Press)

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Abstract

Let Sm−1 be the simplex in Rm , and V:Sm−1→Sm−1 be a nonlinear mapping then this operator satisfies an ergodic theorem if the limit limn→∞1n∑k=1nVk(x) exists for every x∈Sm−1 . It is a well known fact that this ergodicity may fail for Volterra quadratic operators, so it is natural to characterize all non-ergodic operators. However, there is an ongoing problem even in the low dimensional simplexes. In this paper, we solve the mentioned problem within Volterra cubic stochastic operators acting on two-dimensional simplex.

Item Type: Article (Journal)
Additional Information: 5826/73972
Uncontrolled Keywords: Cubic stochastic operator Volterra operator Non-ergodic Dynamics This is a preview of subscription content, log in to check access.
Subjects: Q Science > QA Mathematics
Kulliyyahs/Centres/Divisions/Institutes (Can select more than one option. Press CONTROL button): Kulliyyah of Science
Kulliyyah of Science > Department of Computational and Theoretical Sciences
Depositing User: DR. CHIN HEE PAH
Date Deposited: 11 Sep 2019 09:03
Last Modified: 11 Sep 2019 09:05
URI: http://irep.iium.edu.my/id/eprint/73972

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