Classification of ξ ( s ) -Quadratic Stochastic Operators on 2D simplex (original) (raw)
Related papers
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 -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 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 ξ s -quadratic stochastic operators in 2-dimensional simplex
In this paper we introduce a new class of quadratic stochastic operators called ξ s-QSO. We first classify such operators on 2D-simplex, into six non-isomorphic classes, with respect to their conjugacy and renumeration of the coordinates. Moreover, we investigate the behaviour of operators from two classes.
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.
Classification of a new subclass of ξ(as)-QSO and its dynamics
Journal of Mathematics and Computer Science, 2017
A quadratic stochastic operator (QSO) describes the time evolution of different species in biology. The main problem with regard to a nonlinear operator is to study its behavior. This subject has not been studied in depth; even QSOs, which are the simplest nonlinear operators, have not been studied thoroughly. In this paper we introduce a new subclass of ξ (as)-QSO defined on 2D simplex. first we classify this subclass into 18 non-conjugate classes. Furthermore, we investigate the behavior of one class.
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 Volterra and orthoganality preserving quadratic stochastic operators
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. In the present paper, we first give a simple characterization of Volterra QSO in terms of absolutely continuity of discrete measures. Moreover, we provide its generalization in continuous setting. Further, we introduce a notion of orthogonal preserving QSO, and describe such kind of operators defined on two dimensional simplex. It turns out that orthogonal preserving QSOs are permutations of Volterra QSO. The associativity of genetic algebras generated by orthogonal preserving QSO is studied too.