2017
Том 69
№ 9

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Volterra quadratic stochastic operators of a two-sex population

Rozikov U. A., Zhamilov U. U.

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Abstract

We introduce the notion of Volterra quadratic stochastic operators of a bisexual population. The description of the fixed points of Volterra quadratic stochastic operators of a bisexual 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 bisexual 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 bisexual population is a convex compact set, and the extreme points of this set are found. Volterra quadratic stochastic operators of a bisexual population that have a 2-periodic orbit (trajectory) are constructed.

English version (Springer): Ukrainian Mathematical Journal 63 (2011), no. 7, pp 1136-1153.

Citation Example: Rozikov U. A., Zhamilov U. U. Volterra quadratic stochastic operators of a two-sex population // Ukr. Mat. Zh. - 2011. - 63, № 7. - pp. 985-998.

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