We introduce the notion of Volterra quadratic stochastic operators of a two-sex population. The description of the fixed points of Volterra quadratic stochastic operators of a two-sex population is reduced to the description of the fixed points of Volterra-type operators. Several Lyapunov functions are constructed for the Volterra quadratic stochastic operators of a two-sex population. By using these functions, we obtain an upper bound for the ω-limit set of trajectories. It is shown that the set of all Volterra quadratic stochastic operators of a two-sex population is a convex compact set, and the extreme points of this set are found. Volterra quadratic stochastic operators of a two-sex population that have a 2-periodic orbit (trajectory) are constructed.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 63, No. 7, pp. 985–998, July, 2011.
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Rozikov, U.A., Zhamilov, U.U. Volterra quadratic stochastic operators of a two-sex population. Ukr Math J 63, 1136–1153 (2011). https://doi.org/10.1007/s11253-011-0568-y
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DOI: https://doi.org/10.1007/s11253-011-0568-y