On ξ s -quadratic stochastic operators in 2-dimensional simplex (original) (raw)
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Classification of ξ ( s ) -Quadratic Stochastic Operators on 2D simplex
Journal of Physics: Conference Series, 2013
A quadratic stochastic operator (in short QSO) is usually used to present the time evolution of differing species in biology. Some QSO has been studied by Lotka and Volterra. The general problem in the nonlinear operator theory is to study the behavior of operators. This problem was not fully finished even for the quadratic stochastic operators. To study this problem it was investigated several classes of such QSO. In this paper we study ξ (s) -QSO class of operators. We study such kind of operators on 2D simplex. We first classify these ξ (s) -QSO into 20 classes. Further, we investigate the dynamics of one class of such operators.
Onξ(s)-Quadratic Stochastic Operators on Two-Dimensional Simplex and Their Behavior
Abstract and Applied Analysis, 2013
A quadratic stochastic operator (in short QSO) is usually used to present the time evolution of differing species in biology. Some quadratic stochastic operators have been studied by Lotka and Volterra. The general problem in the nonlinear operator theory is to study the behavior of operators. This problem was not fully finished even for quadratic stochastic operators which are the simplest nonlinear operators. To study this problem, several classes of QSO were investigated. We studyξ(s)-QSO defined on 2D simplex. We first classifyξ(s)-QSO into 20 nonconjugate classes. Further, we investigate the dynamics of three classes of such operators.
On ξa -quadratic stochastic operators on 2-D simplex
2014
A quadratic stochastic operator (QSO) is usually used to present the time evolution of differing species in biology. Some quadratic stochastic operators have been studied by Lotka and Volterra. The general problem in the nonlinear operator theory is to study the behavior of operators. This problem was not fully finished even for quadratic stochastic operators which are the simplest nonlinear operators. To study this problem, several classes of QSO were investigated. In this paper, we study the ξ (a)-QSO defined on 2D simplex. We first classify ξ (a)-QSO into 2 non-conjugate classes. Further, we investigate the dynamics of these classes of such operators.
2014
A quadratic stochastic operator (QSO) is usually used to present the time evolution of differing species in biology. Some quadratic stochastic operators have been studied by Lotka and Volterra. The general problem in the nonlinear operator theory is to study the behavior of operators. This problem was not fully finished even for quadratic stochastic operators which are the simplest nonlinear operators. To study this problem, several classes of QSO were investigated. In this paper, we study the ξ(a)–QSO defined on 2D simplex. We first classify ξ(a)–QSO into 2 non-conjugate classes. Further, we investigate the dynamics of these classes of such operators.
On xi-(s) quadratic stochastic operators on two-dimensionalsimplex and their behavior
2013
A quadratic stochastic operator (in short QSO) is usually used to present the time evolution of differing species in biology. Some quadratic stochastic operators have been studied by Lotka and Volterra. The general problem in the nonlinear operator theory is to study the behavior of operators. This problem was not fully finished even for quadratic stochastic operators which are the simplest nonlinear operators. To study this problem, several classes of QSO were investigated. We study ( ) -QSO defined on 2D simplex. We first classify ( ) -QSO into 20 nonconjugate classes. Further, we investigate the dynamics of three classes of such operators.
On -Quadratic Stochastic Operators on Two-Dimensional Simplex and Their Behavior
Abstract and Applied Analysis, 2013
A quadratic stochastic operator (in short QSO) is usually used to present the time evolution of differing species in biology. Some quadratic stochastic operators have been studied by Lotka and Volterra. The general problem in the nonlinear operator theory is to study the behavior of operators. This problem was not fully finished even for quadratic stochastic operators which are the simplest nonlinear operators. To study this problem, several classes of QSO were investigated. We study ( ) -QSO defined on 2D simplex. We first classify ( ) -QSO into 20 nonconjugate classes. Further, we investigate the dynamics of three classes of such operators.
ON DYNAMICS OF ξ S QUADRATIC STOCHASTIC OPERATORS
International Journal of Modern Physics: Conference Series, 2012
In this research we introduce a new class of quadratic stochastic operators called ξ s -QSO which are defined through coefficient of the operator from measure-theoretic (namely we are looking the coefficient as the measures which are absolute continuous or singular) point of view. We also study the limiting behaviour of ξ s -QSO defined on 2D-simplex. We first describe ξ s -QSO on 2Dsimplex and classify them with respect to the conjugacy and renumeration of the coordinates. We find six non-isomorphic classes of such operators. Moreover, we investigate the behaviour of each operator from three classes and prove convergence of trajectories of these classes and study their certain properties. We showed trajectories of two classes converge to the equilibrium. For the third class, it is established only the negative trajectories converge to the equilibrium.
On orthogonality preserving cubic stochastic operator defined on 1-dimensional simplex
PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON MATHEMATICAL SCIENCES AND TECHNOLOGY 2018 (MATHTECH2018): Innovative Technologies for Mathematics & Mathematics for Technological Innovation
In this paper, we consider the cubic stochastic operator (CSO) defined on 1-dimensional simplex, S 1. We provide a full description of orthogonal preserving (OP) cubic stochastic operators on the simplex. We provide full description of the fixed points subject to two different parameters for the Volterra OP CSO on the simplex. In the last section we describe the behaviour of the fixed points.
Classification and study of a new class of $ \xi^{(as)} $-QSO
arXiv: Dynamical Systems, 2018
Many systems are presented using theory of nonlinear operators. A quadratic stochastic operator (QSO) is perceived as a nonlinear operator. It has a wide range of applications in various disciplines, such as mathematics, biology, and other sciences. The central problem that surrounds this nonlinear operator lies in the requirement that behavior should be studied. Nonlinear operators, even QSO (i.e., the simplest nonlinear operator), have not been thoroughly investigated. This study aims to present a new class of xi(as)\xi^{(as)}xi(as)-QSO defined on 2D simplex and to classify it into 18 non-conjugate (isomorphic) classes based on their conjugacy and the remuneration of coordinates. In addition, the limiting points of the behavior of trajectories for four classes defined on 2D simplex are examined.
On Quadratic Stochastic Operators Having Three Fixed Points
Journal of Physics: Conference Series, 2016
We knew that a trajectory of a linear stochastic operator associated with a positive square stochastic matrix starting from any initial point from the simplex converges to a unique fixed point. However, in general, the similar result for a quadratic stochastic operator associated with a positive cubic stochastic matrix does not hold true. In this paper, we provide an example for the quadratic stochastic operator with positive coefficients in which its trajectory may converge to different fixed points depending on initial points.