On the dynamics of non-Volterra quadratic operators corresponding to permutations
Uygun JamilovDepartment Algebra and Functional Analysis, National University of Uzbekistan, Tashkent, UzbekistanKh. O. KhudoyberdievV.I. Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences, Tashkent, Uzbekistan
ABI
Abstract
The present paper deals to a family of non-Volterra quadratic stochastic operators depending on a parameter and a permutation and their trajectory behaviours. We find all fixed and periodic points for such non-Volterra quadratic stochastic operator on a finite-dimensional simplex. We proved that the ω- limit set of any trajectory of such non-Volterra quadratic stochastic operator consists of either single point or finite points.
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