Statistical solution and Liouville-type theorem for the nonautonomous discrete Selkov model

IF 0.5 4区数学 Q4 MATHEMATICS, APPLIED

Dynamical Systems-An International Journal Pub Date : 2022-11-28 DOI:10.1080/14689367.2022.2147811

Congcong Li, Chunqiu Li, Jintao Wang

引用次数: 1

Abstract

In this article, we study the statistical solution of the nonautonomous discrete Selkov model. First, we show the existence of a pullback- attractor for the system and establish the existence of a unique family of invariant Borel probability measures carried by the pullback- attractor. Then we further prove that the family of invariant Borel probability measures is a statistical solution for the discrete system and satisfies a Liouville-type theorem. Finally, we demonstrate that the invariant property of the statistical solution is indeed a particular case of the Liouville-type theorem.

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非自治离散Selkov模型的统计解和liouville型定理

本文研究了非自治离散Selkov模型的统计解。首先，我们证明了系统的回调吸引子的存在性，并建立了由该回调吸引子携带的不变Borel概率测度的唯一族的存在性。然后我们进一步证明了不变Borel概率测度族是离散系统的统计解，并且满足刘维尔型定理。最后，我们证明了统计解的不变性质确实是刘维尔型定理的一个特例。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Dynamical Systems-An International Journal 物理-力学

CiteScore

0.90

自引率

0.00%

发文量

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