2019
Том 71
№ 7

All Issues

Zhamilov U. U.

Articles: 2
Brief Communications (Russian)

Nonergodic Quadratic Operators for a Two-Sex Population

Ganikhodzhaev N. N., Mukhitdinov R. T., Zhamilov U. U.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2013. - 65, № 8. - pp. 1152–1160

We describe the structure of quadratic operators of a two-sex population that differs from the model studied by Lyubich and give an example of nonergodic quadratic operator for a two-sex population.

Article (Russian)

Volterra quadratic stochastic operators of a two-sex population

Rozikov U. A., Zhamilov U. U.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2011. - 63, № 7. - pp. 985-998

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.