{"title":"Influences of artificial numerical noise on statistics and qualitative properties of chaotic system","authors":"","doi":"10.1016/j.physd.2024.134355","DOIUrl":null,"url":null,"abstract":"<div><p>Taking the nonlinear Schrödinger equation (NLSE) as an example, we provide from a mathematical viewpoint, rigorous evidence that numerical noise of a chaotic system as tiny artificial stochastic disturbances can increase exponentially to a macro-level. As a result, numerical simulations given by traditional algorithms in double precision may rapidly become badly polluted leading to huge deviations from the ‘true’ solution not only in trajectory but also, sometimes, even in statistics and/or some qualitative properties. Small physical disturbances in time and space are unavoidable in practice, which are often much larger than artificial numerical noise. So, from a physical viewpoint, it is wrong to neglect small spatio-temporal disturbances of a chaotic system: chaos should not be described by deterministic equations.</p></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":null,"pages":null},"PeriodicalIF":2.7000,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physica D: Nonlinear Phenomena","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0167278924003051","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
Taking the nonlinear Schrödinger equation (NLSE) as an example, we provide from a mathematical viewpoint, rigorous evidence that numerical noise of a chaotic system as tiny artificial stochastic disturbances can increase exponentially to a macro-level. As a result, numerical simulations given by traditional algorithms in double precision may rapidly become badly polluted leading to huge deviations from the ‘true’ solution not only in trajectory but also, sometimes, even in statistics and/or some qualitative properties. Small physical disturbances in time and space are unavoidable in practice, which are often much larger than artificial numerical noise. So, from a physical viewpoint, it is wrong to neglect small spatio-temporal disturbances of a chaotic system: chaos should not be described by deterministic equations.
期刊介绍：
Physica D (Nonlinear Phenomena) publishes research and review articles reporting on experimental and theoretical works, techniques and ideas that advance the understanding of nonlinear phenomena. Topics encompass wave motion in physical, chemical and biological systems; physical or biological phenomena governed by nonlinear field equations, including hydrodynamics and turbulence; pattern formation and cooperative phenomena; instability, bifurcations, chaos, and space-time disorder; integrable/Hamiltonian systems; asymptotic analysis and, more generally, mathematical methods for nonlinear systems.
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
