[ספר][B] Gibbs measures in biology and physics: The Potts model

UA Rozikov - 2022‏ - World Scientific
In this chapter we give main definitions and useful facts of the theory of Gibbs measures of
lattice spin systems. In the first section we give general definitions. This chapter also …

[ספר][B] Population dynamics: algebraic and probabilistic approach

UA Rozikov - 2020‏ - World Scientific
In this chapter we give some minimal preliminaries from biology, motivations of studying of
population dynamics, and define evolution operators and associated algebras related to free …

Quadratic stochastic processes of type

BJ Mamurov, UA Rozikov, SS Xudayarov - arxiv preprint arxiv …, 2020‏ - arxiv.org
We construct quadratic stochastic processes (QSP)(also known as Markov processes of
cubic matrices) in continuous and discrete times. These are dynamical systems given by (a …

Ergodicity of nonlinear Markov operators on the finite dimensional space

M Saburov - Nonlinear Analysis: Theory, Methods & Applications, 2016‏ - Elsevier
A nonlinear Markov chain is a discrete time stochastic process whose transition matrices
may depend not only on the current state of the process but also on the current distribution of …

On a family of strictly non-Volterra quadratic stochastic operators

U Jamilov - Journal of Physics: Conference Series, 2016‏ - iopscience.iop.org
On a Family of Strictly Non-Volterra Quadratic Stochastic Operators Page 1 Journal of Physics:
Conference Series PAPER • OPEN ACCESS On a Family of Strictly Non-Volterra Quadratic …

On Nonergodic Uniform Lotka–Volterra Operators.

FM Mukhamedov, UU Jamilov… - Mathematical …, 2019‏ - search.ebscohost.com
On Nonergodic Uniform Lotka–Volterra Operators* Page 1 ISSN 0001-4346, Mathematical Notes,
2019, Vol. 105, No. 2, pp. 258–264. © Pleiades Publishing, Ltd., 2019. On Nonergodic Uniform …

Quadratic operators corresponding to permutations

UU Jamilov, KO Khudoyberdiev… - Stochastic Analysis and …, 2020‏ - Taylor & Francis
In the present paper we consider a family of non-Volterra quadratic stochastic operators
depending on a parameter α and study their trajectory behaviors. We find all fixed and …

Genetic Algebras Associated with ξ(a)-Quadratic Stochastic Operators

F Mukhamedov, I Qaralleh, T Qaisar, MA Hasan - Entropy, 2023‏ - mdpi.com
The present paper deals with a class of ξ (a)-quadratic stochastic operators, referred to as
QSOs, on a two-dimensional simplex. It investigates the algebraic properties of the genetic …

Genetic Volterra algebras and their derivations

R Ganikhodzhaev, F Mukhamedov… - Communications in …, 2018‏ - Taylor & Francis
The present paper is devoted to genetic Volterra algebras. We first study characters of such
algebras. We fully describe associative genetic Volterra algebras, in this case all derivations …

A flow of quantum genetic Lotka-Volterra algebras on M2 (C)

F Mukhamedov, SM Syam, I Qaralleh - Journal of Geometry and Physics, 2023‏ - Elsevier
In the present paper, we define a quantum analog of Lotka-Volterra algebras using a
coalgebra scheme. This new framework provides a fresh perspective for the treatment of …