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Dynamics of composition of two quadratic stochastic Volterra operators

Ganikhodzaev, Rasul and Mukhamedov, Farrukh and Saburov, Mansoor and Qaralleh, Izzat (2013) Dynamics of composition of two quadratic stochastic Volterra operators. In: International Conference On Mathematical Sciences And Statistics 2013, 5-7 February 2013, Kuala Lumpur.

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One of the simplest unsolved problems in the theory of nonlinear dynamical systems is to study asymptotic behaviors of quadratic stochastic operators (in short QSO) on the finite dimensional simplex. However, this problem is not fully finished even in 2D case. The reason is that, in such systems, we may observe some chaotic behaviors (more precisely, Li-Yorke chaotic behaviors). It is worth mentioning that the square of some quadratic homeomorphisms of the simplex are topologically conjugate to compositions of two distinct Volterra QSO. Therefore, it is of independent interest to study the asymptotical behavior of the composition of two Volterra QSO. In this paper, we shall present some unexpected asymptotical behaviors. For example, we can see some interesting asymptotical behavior of composition of regular (stable) and chaotic (or unstable) Volterra quadratic stochastic operators. Our obtained results enable to study general problems in the theory of quadratic stochastic operators.

Item Type: Conference or Workshop Item (Full Paper)
Additional Information: 6769/28933
Uncontrolled Keywords: Quadratic stochastic operator; Volterra operator; Composition; Asymptotical behavior.
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 Mansoor Saburov
Date Deposited: 15 Feb 2013 13:05
Last Modified: 15 Feb 2013 13:05
URI: http://irep.iium.edu.my/id/eprint/28933

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