The approximation and portray of stochastic Poincaré maps for stochastic slow-fast systems in Hilbert spaces

IF 1.1 2区 数学 Q1 MATHEMATICS
Min Yang, Guanggan Chen
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引用次数: 0

Abstract

This work is concerned with the stochastic slow-fast evolutionary systems with white noises in Hilbert spaces. We first establish the stochastic Poincaré maps of the stochastic slow-fast systems in the neighborhood of the periodic orbit for the approximate systems with colored noises in distribution. Further employing the random slow manifold theory, we prove that the stochastic Poincaré maps of the stochastic slow-fast systems converge to the same fixed point of the stochastic Poincaré maps for the approximate systems in distribution as the colored noise parameter tends to zero. Moreover, we apply the moving orthonormal system to construct the exact portray of the stochastic Poincaré maps for the stochastic slow-fast systems in distribution. A concrete example is provided to illustrate the stochastic Poincaré maps.

希尔伯特空间中随机慢速系统的随机波因卡雷映射的近似与刻画
本研究关注希尔伯特空间中具有白噪声的随机慢-快演化系统。我们首先建立了周期轨道邻域内随机慢速系统的随机 Poincaré 映射,用于近似分布有彩色噪声的系统。我们进一步利用随机慢流形理论证明,当彩色噪声参数趋近于零时,随机慢速系统的随机 Poincaré 映射收敛到分布中近似系统的随机 Poincaré 映射的相同固定点。此外,我们还应用移动正交系统构建了分布中随机慢速系统的随机波因卡雷图的精确描绘。我们提供了一个具体的例子来说明随机 Poincaré 地图。
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
CiteScore
2.00
自引率
8.30%
发文量
67
审稿时长
>12 weeks
期刊介绍: The Banach Journal of Mathematical Analysis (Banach J. Math. Anal.) is published by Birkhäuser on behalf of the Tusi Mathematical Research Group. Banach J. Math. Anal. is a peer-reviewed electronic journal publishing papers of high standards with deep results, new ideas, profound impact, and significant implications in all areas of functional analysis and operator theory and all modern related topics. Banach J. Math. Anal. normally publishes survey articles and original research papers numbering 15 pages or more in the journal’s style. Shorter papers may be submitted to the Annals of Functional Analysis or Advances in Operator Theory.
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