Dynamics of composition of two quadratic stochastic Volterra operators

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...

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Main Authors:	Ganikhodzaev, Rasul, Mukhamedov, Farrukh, Saburov, Mansoor, Qaralleh, Izzat
Format:	Conference or Workshop Item
Language:	English
Published:	2013
Subjects:	QA Mathematics
Online Access:	http://irep.iium.edu.my/28933/ http://irep.iium.edu.my/28933/ http://irep.iium.edu.my/28933/1/Composition_of_QSO--ICMSS2013.pdf

id	iium-28933
recordtype	eprints
spelling	iium-289332013-02-15T05:05:50Z http://irep.iium.edu.my/28933/ Dynamics of composition of two quadratic stochastic Volterra operators Ganikhodzaev, Rasul Mukhamedov, Farrukh Saburov, Mansoor Qaralleh, Izzat QA Mathematics 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. 2013-02-05 Conference or Workshop Item PeerReviewed application/pdf en http://irep.iium.edu.my/28933/1/Composition_of_QSO--ICMSS2013.pdf 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. http://math.upm.edu.my/icmss2013/
repository_type	Digital Repository
institution_category	Local University
institution	International Islamic University Malaysia
building	IIUM Repository
collection	Online Access
language	English
topic	QA Mathematics
spellingShingle	QA Mathematics Ganikhodzaev, Rasul Mukhamedov, Farrukh Saburov, Mansoor Qaralleh, Izzat Dynamics of composition of two quadratic stochastic Volterra operators
description	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.
format	Conference or Workshop Item
author	Ganikhodzaev, Rasul Mukhamedov, Farrukh Saburov, Mansoor Qaralleh, Izzat
author_facet	Ganikhodzaev, Rasul Mukhamedov, Farrukh Saburov, Mansoor Qaralleh, Izzat
author_sort	Ganikhodzaev, Rasul
title	Dynamics of composition of two quadratic stochastic Volterra operators
title_short	Dynamics of composition of two quadratic stochastic Volterra operators
title_full	Dynamics of composition of two quadratic stochastic Volterra operators
title_fullStr	Dynamics of composition of two quadratic stochastic Volterra operators
title_full_unstemmed	Dynamics of composition of two quadratic stochastic Volterra operators
title_sort	dynamics of composition of two quadratic stochastic volterra operators
publishDate	2013
url	http://irep.iium.edu.my/28933/ http://irep.iium.edu.my/28933/ http://irep.iium.edu.my/28933/1/Composition_of_QSO--ICMSS2013.pdf
first_indexed	2023-09-18T20:42:30Z
last_indexed	2023-09-18T20:42:30Z
_version_	1777409458535661568

Dynamics of composition of two quadratic stochastic Volterra operators

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