Discontinuity, Nonlinearity, and Complexity
On Symmetric Strictly nonVolterra Quadratic Stochastic Operators
Discontinuity, Nonlinearity, and Complexity 5(3) (2016) 263283  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 nonVolterra quadratic stochastic operator on the threedimensional 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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