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.