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...
| Main Authors: | , , , |
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| Format: | Proceeding Paper |
| Language: | English |
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2013
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| Online Access: | http://irep.iium.edu.my/28933/ http://irep.iium.edu.my/28933/1/Composition_of_QSO--ICMSS2013.pdf |
| _version_ | 1848780036559077376 |
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| author | Ganikhodzaev, Rasul Mukhamedov, Farrukh Saburov, Mansoor Qaralleh, Izzat |
| author_facet | Ganikhodzaev, Rasul Mukhamedov, Farrukh Saburov, Mansoor Qaralleh, Izzat |
| author_sort | Ganikhodzaev, Rasul |
| building | IIUM Repository |
| collection | Online Access |
| 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. |
| first_indexed | 2025-11-14T15:27:17Z |
| format | Proceeding Paper |
| id | iium-28933 |
| institution | International Islamic University Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T15:27:17Z |
| publishDate | 2013 |
| recordtype | eprints |
| repository_type | Digital Repository |
| 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 Proceeding Paper 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/ |
| spellingShingle | QA Mathematics Ganikhodzaev, Rasul Mukhamedov, Farrukh Saburov, Mansoor Qaralleh, Izzat Dynamics of composition of two quadratic stochastic Volterra operators |
| title | 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_short | Dynamics of composition of two quadratic stochastic Volterra operators |
| title_sort | dynamics of composition of two quadratic stochastic volterra operators |
| topic | QA Mathematics |
| 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 |