2019
Том 71
№ 8

All Issues

Rozikov U. A.

Articles: 3
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.

Brief Communications (Russian)

On Cubic Operators Defined on Finite-Dimensional Simplexes

Rozikov U. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2004. - 56, № 10. - pp. 1424-1433

We introduce the concept of cubic operator. For one class of cubic operators defined on finite-dimensional simplexes, a complete description of the behavior of their trajectories is given. The convergence of Cesaro means is established.

Article (Russian)

Random Walks in Random Media on a Cayley Tree

Rozikov U. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2001. - 53, № 10. - pp. 1391-1401

We present sufficient conditions for the transience of random walks with bounded jumps in random media on a Cayley tree.