About Two-Dimensional QNSO

Abstract

In the world, many scientific and practical problems in dynamical systems are modeled by evolutionary operators of stochastic and non-stochastic cubic matrices. In many biological and physical systems their behaviour can be given by dynamics of quadratic (non-)stochastic operators defined by cubic matrices. A quadratic stochastic process is defined by a family of cubic matrices which satisfy Kolmogorov-Chapman equation with respect to a fixed multiplication and stochastisity of such matrices. Therefore, the study of the dynamics of nonlinear operators constructed using stochastic and non-stochastic cubic matrices that preserve simplex remains one of the important and urgent tasks. In the book [12] entitled “Population dynamics: algebraic and probabilistic approach” which is written by U. A.Rozikov in 2020, the probabilistic approach part presents Markov processes of cubic stochastic (in a fixed sense) matrices (MPCSM), which are continuous-time dynamical systems, whose states are stochastic cubic matrices satisfying an analogue of the Kolmogorov-Chapman equation. MPCSM considered for two specially chosen notions of stochastic cubic matrices and two Maksimov’s multiplications of such matrices.Time-dependent behavior of such processes is given with applications to a population with the possibility of twin births