# The dynamics of superposition of volterra and permuted volterra quadratic stochastic operators

## The dynamics of superposition of volterra and permuted volterra quadratic stochastic operators

## Abstract

The concept of a quadratic stochastic operator and its application in a biological context were first

established by Bernstein in [1]. Since then, the theory of quadratic stochastic operators has been further

deepened motivated by their frequent occurrence in mathematical models of genetics, where quadratic

stochastic operators serve as a tool for the study of dynamical properties and modelling; see e.g. [2,3,4].

## References

Bernstein S., Solution of a mathematical problem connected with the theory of heredity. The Annals of

Mathematical Statistics. (1942), 13(1), 53–61.

Ganikhodzhaev R.N., Quadratic stochastic operators, Lyapunov functions and tournaments. Sb. Math.

(1993), 76(2), 489–506 .

Ganikhodzhaev N.N., Ganikhodzhaev R.N. and Jamilov U.U., Quadratic stochastic operators and zerosum game dynamics. Ergod. Th. and Dynam. Sys. (2015), 35(5), 1443–1473.

Jamilov U. U., Quadratic stochastic operators corresponding to graphs. Lobachevskii J. Math. (2013).

(2), 148-151.

## Published

## How to Cite

*MODERN PROBLEMS AND PROSPECTS OF APPLIED MATHEMATICS*,

*1*(01). Retrieved from https://ojs.qarshidu.uz/index.php/mp/article/view/553