An operator methodology for the global dynamic analysis of stochastic nonlinear systems

IF 3.2 3区 工程技术 Q2 MECHANICS Theoretical and Applied Mechanics Letters Pub Date : 2023-05-01 DOI:10.1016/j.taml.2022.100419
Kaio C. B. Benedetti , Paulo B. Gonçalves , Stefano Lenci , Giuseppe Rega
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引用次数: 5

Abstract

In a global dynamic analysis, the coexisting attractors and their basins are the main tools to understand the system behavior and safety. However, both basins and attractors can be drastically influenced by uncertainties. The aim of this work is to illustrate a methodology for the global dynamic analysis of nondeterministic dynamical systems with competing attractors. Accordingly, analytical and numerical tools for calculation of nondeterministic global structures, namely attractors and basins, are proposed. First, based on the definition of the Perron-Frobenius, Koopman and Foias linear operators, a global dynamic description through phase-space operators is presented for both deterministic and nondeterministic cases. In this context, the stochastic basins of attraction and attractors’ distributions replace the usual basin and attractor concepts. Then, numerical implementation of these concepts is accomplished via an adaptative phase-space discretization strategy based on the classical Ulam method. Sample results of the methodology are presented for a canonical dynamical system.

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随机非线性系统全局动态分析的算子方法学
在全局动力学分析中,共存吸引子及其盆地是了解系统行为和安全性的主要工具。然而,盆地和吸引子都可能受到不确定性的极大影响。这项工作的目的是说明具有竞争吸引子的不确定性动力系统的全局动态分析的方法。在此基础上,提出了不确定性全局结构(吸引子和盆地)的解析和数值计算工具。首先,基于Perron-Frobenius、Koopman和Foias线性算子的定义,给出了确定性和非确定性情况下的相空间算子全局动态描述。在这种情况下,吸引子和吸引子分布的随机盆地取代了通常的盆地和吸引子概念。然后,通过基于经典Ulam方法的自适应相空间离散策略实现了这些概念的数值实现。给出了典型动力系统的实例结果。
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来源期刊
CiteScore
6.20
自引率
2.90%
发文量
545
审稿时长
12 weeks
期刊介绍: An international journal devoted to rapid communications on novel and original research in the field of mechanics. TAML aims at publishing novel, cutting edge researches in theoretical, computational, and experimental mechanics. The journal provides fast publication of letter-sized articles and invited reviews within 3 months. We emphasize highlighting advances in science, engineering, and technology with originality and rapidity. Contributions include, but are not limited to, a variety of topics such as: • Aerospace and Aeronautical Engineering • Coastal and Ocean Engineering • Environment and Energy Engineering • Material and Structure Engineering • Biomedical Engineering • Mechanical and Transportation Engineering • Civil and Hydraulic Engineering Theoretical and Applied Mechanics Letters (TAML) was launched in 2011 and sponsored by Institute of Mechanics, Chinese Academy of Sciences (IMCAS) and The Chinese Society of Theoretical and Applied Mechanics (CSTAM). It is the official publication the Beijing International Center for Theoretical and Applied Mechanics (BICTAM).
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