关于Volterra和非Volterra三次随机算子的动力学

IF 0.5 4区 数学 Q4 MATHEMATICS, APPLIED Dynamical Systems-An International Journal Pub Date : 2021-11-18 DOI:10.1080/14689367.2021.2006150
U. Jamilov, A. Y. Khamrayev
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引用次数: 0

摘要

我们考虑Volterra和非Volterra三次随机算子。对于定义在二维单纯形上的Volterra三次随机算子,证明了单纯形的顶点和中心是不动点。这样的算子从单纯形边界的任何点开始的轨迹是收敛的,并且这样的算子的轨迹从单纯形内部的任何点(除了中心)开始的轨迹不收敛。此外,其中证明了任何轨迹的平均值都不收敛。对于定义在二维单纯形上的非Volterra三次随机算子,证明了不动点的唯一性,该不动点是排斥的,并且从单纯形边界开始的任何轨迹都收敛到由单纯形的三个顶点组成的周期轨迹。除中心外,从单纯形内部开始的轨迹的极限点集是单纯形边界的无限子集。
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On dynamics of Volterra and non-Volterra cubic stochastic operators
We consider Volterra and non-Volterra cubic stochastic operators. For a Volterra cubic stochastic operator defined on the two-dimensional simplex, it is shown that the vertices and the centre of the simplex are fixed points. The trajectory of such an operator starting from any point from the boundary of the simplex is convergent, and the trajectory of such an operator starting from any point from the interior of the simplex except the centre does not converge. Moreover, therein proven the mean of any trajectory does not converge. For a non-Volterra cubic stochastic operator defined on the two-dimensional simplex, it is proved that the uniqueness of a fixed point, which is repelling and any trajectory starting from the boundary of the simplex converges to a periodic trajectory which consists of three vertices of the simplex. The set of limit points of the trajectory starting from the interior of the simplex except the centre is an infinite subset of the boundary of the simplex.
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来源期刊
CiteScore
0.90
自引率
0.00%
发文量
33
审稿时长
>12 weeks
期刊介绍: Dynamical Systems: An International Journal is a world-leading journal acting as a forum for communication across all branches of modern dynamical systems, and especially as a platform to facilitate interaction between theory and applications. This journal publishes high quality research articles in the theory and applications of dynamical systems, especially (but not exclusively) nonlinear systems. Advances in the following topics are addressed by the journal: •Differential equations •Bifurcation theory •Hamiltonian and Lagrangian dynamics •Hyperbolic dynamics •Ergodic theory •Topological and smooth dynamics •Random dynamical systems •Applications in technology, engineering and natural and life sciences
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