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ISSN:2164-6376 (print)
ISSN:2164-6414 (online)
Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

Email: dumitru.baleanu@gmail.com

On Symmetric Strictly non-Volterra Quadratic Stochastic Operators

Discontinuity, Nonlinearity, and Complexity 5(3) (2016) 263--283 | DOI:10.5890/DNC.2016.09.006

U.U. Jamilov

Institute of Mathematics, National University of Uzbekistan, 29, Do’rmon Yo’li str., 100125, Tashkent, Uzbekistan

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Abstract

For a symmetric strictly non-Volterra quadratic stochastic operator on the three-dimensional simplex it is proved that this operator has a unique fixed point. A sufficient condition of attractiveness for the unique fixed point is found. For such operators we describe the set of ω− limit points. We proved that some classes of such operators have infinitely many periodic points. Also it is shown that there are trajectories which are asymptotically cyclic with period two.

Acknowledgments

The Author grateful to professors U. A. Rozikov, J. Blath and M. Scheutzow for helpful discussions. He thanks IMU Berlin Einstein Foundation Program (EFP), Berlin Mathematical School(BMS) for scholarship and for support of his visit to Technical University(TU) Berlin and TU Berlin for kind hospitality.

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