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Discontinuity, Nonlinearity, and Complexity 10(1) (2021) 43--60 | DOI:10.5890/DNC.2021.03.004

N.N. Ganikhodjaev$^{1}$, U.U. Jamilov$^{2}$ , M. Ladra$^{3}$

$^1$ Department of Computational and Theoretical Sciences, Faculty of Science, IIUM, 25200 Kuantan, Malaysia

$^2$ V.I. Romanovskiy Institute of Mathematics, 100170, Tashkent, Uzbekistan

$^3$ Department of Algebra, University of Santiago de Compostela, Spain

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Abstract

In this paper we consider the quadratic stochastic operators describing evolution of a bisexual population. We establish correlation between such operators and evolutionary games, namely demonstrate that Volterra quadratic stochastic operator with degenerate payoff matrix is non-ergodic and corresponding evolutionary game is rock-paper-scissors game. To prove this statements we study the asymptotic behavior of trajectories of the Volterra quadratic stochastic operators with the non-hyperbolic fixed points.

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