Classification and study of a new class of $ \xi^{(as)} $-QSO (original) (raw)
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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.
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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.
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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.
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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.
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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.
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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 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.
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The Journal of Nonlinear Sciences and Applications, 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 has not been studied in depth; even QSOs, which are the simplest nonlinear operators, have not been studied thoroughly. This paper investigates the global behavior of an operator taken from ξ (s)-QSO when the parameter a = 1 2. Moreover, we study the local behavior of this operator at each value of a, where 0 < a < 1.