The dynamics of superposition of non-Volterra quadratic stochastic operators
K. A. AralovaV.I. Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences, Tashkent, UzbekistanUygun JamilovMathematics, National University of Uzbekistan, Tashkent, Uzbekistan
ABI
Abstract
In the present paper, we study dynamical systems generated by stochastic operators which are superpositions of non-Volterra quadratic stochastic operators defined on the two-dimensional simplex. We showed that such stochastic operators have two fixed points and there are no periodic points except fixed points. We showed that any trajectory of such an operator converges to a fixed point. Thus, these operators are ergodic transformations.
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