Journal of Computational Dynamics最新文献_第2页

Preface: Special issue on continuation methods and applications 前言延续方法与应用特刊

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Journal of Computational Dynamics Pub Date : 2022-01-01 DOI: 10.3934/jcd.2022015

B. Krauskopf, H. Osinga

引用次数: 0

Smooth complete Lyapunov functions for multifunctions 多函数的光滑完全Lyapunov函数

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Journal of Computational Dynamics Pub Date : 2022-01-01 DOI: 10.3934/jcd.2022025

S. Suhr

引用次数: 0

Emergence of quasiperiodic regimes in a neutral delay model of flute-like instruments: Influence of the detuning between resonance frequencies 类笛子乐器中性延迟模型中准周期状态的出现:共振频率之间失谐的影响

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Journal of Computational Dynamics Pub Date : 2022-01-01 DOI: 10.3934/jcd.2022011

S. Terrien, C. Vergez, B. Fabre, P. de la Cuadra

{"title":"Emergence of quasiperiodic regimes in a neutral delay model of flute-like instruments: Influence of the detuning between resonance frequencies","authors":"S. Terrien, C. Vergez, B. Fabre, P. de la Cuadra","doi":"10.3934/jcd.2022011","DOIUrl":"https://doi.org/10.3934/jcd.2022011","url":null,"abstract":"Musical instruments display a wealth of dynamics, from equilibria (where no sound is produced) to a wide diversity of periodic and non-periodic sound regimes. We focus here on two types of flute-like instruments, namely a recorder and a pre-hispanic Chilean flute. A recent experimental study showed that they both produce quasiperiodic sound regimes which are avoided or played on purpose depending on the instrument. We investigate the generic model of sound production in flute-like musical instruments, a system of neutral delay-differential equations. Using time-domain simulations, we show that it produces stable quasiperiodic oscillations in good agreement with experimental observations. A numerical bifurcation analysis is performed, where both the delay time (related to a control parameter) and the detuning between the resonance frequencies of the instrument – a key parameter for instrument makers – are considered as bifurcation parameters. This demonstrates that the large detuning that is characteristic of prehispanic Chilean flutes plays a crucial role in the emergence of stable quasiperiodic oscillations.","PeriodicalId":37526,"journal":{"name":"Journal of Computational Dynamics","volume":"26 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88327269","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Monotonicity and discretization of Hammerstein integrodifference equations Hammerstein积分差分方程的单调性和离散性

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Journal of Computational Dynamics Pub Date : 2022-01-01 DOI: 10.3934/jcd.2022023

Magdalena Nockowska-Rosiak, C. Pötzsche

引用次数: 1

Construction of mean-square Lyapunov-basins for random ordinary differential equations 随机常微分方程的均方lyapunov盆地构造

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Journal of Computational Dynamics Pub Date : 2022-01-01 DOI: 10.3934/jcd.2022024

Florian Rupp

引用次数: 0

Detecting and determining preserved measures and integrals of birational maps 检测和确定两地地图的保存度量和积分

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Journal of Computational Dynamics Pub Date : 2022-01-01 DOI: 10.3934/jcd.2022014

E. Celledoni, C. Evripidou, D. McLaren, B. Owren, G. Quispel, B. Tapley

引用次数: 5

Modified refinement algorithm to construct Lyapunov functions using meshless collocation 改进无网格配置构造Lyapunov函数的改进算法

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Journal of Computational Dynamics Pub Date : 2022-01-01 DOI: 10.3934/jcd.2022022

N. Mohammed, P. Giesl

引用次数: 0

Low-rank kernel approximation of Lyapunov functions using neural networks 利用神经网络的李雅普诺夫函数的低秩核逼近

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Journal of Computational Dynamics Pub Date : 2022-01-01 DOI: 10.3934/jcd.2022026

K. Webster

引用次数: 1

A novel moving orthonormal coordinate-based approach for region of attraction analysis of limit cycles 一种新的基于运动正交坐标的极限环吸引域分析方法

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Journal of Computational Dynamics Pub Date : 2022-01-01 DOI: 10.3934/jcd.2022016

Eva Ahbe, A. Iannelli, Roy S. Smith

{"title":"A novel moving orthonormal coordinate-based approach for region of attraction analysis of limit cycles","authors":"Eva Ahbe, A. Iannelli, Roy S. Smith","doi":"10.3934/jcd.2022016","DOIUrl":"https://doi.org/10.3934/jcd.2022016","url":null,"abstract":"The paper proposes a Lyapunov theory-based method to compute inner estimates of the region of attraction (ROA) of stable limit cycles. The approach is based on a transformation of the system to transverse coordinates, defined on a moving orthonormal coordinate system (MOC) for which a novel construction is presented. The proposed center point MOC (cp-MOC) is associated with a user-defined center point and provides flexibility to the construction of the transverse coordinates. In particular, compared to the standard approach based on hyperplanes orthogonal to the flow, the new construction allows the analyst to obtain larger regions of the state space where the well-definedness property of the transformation is satisfied. This has important benefits when using transverse coordinates to compute inner estimates of the ROA. To demonstrate these improvements, a sum-of-squares optimization-based formulation is proposed for computing inner estimates of the ROA of limit cycles for polynomial dynamics described in transverse coordinates. Different algorithmic options are explored, taking into account computational and accuracy aspects. Results are shown for three different systems exhibiting increasing complexity. The presented algorithms are extensively compared, and the newly cp-MOC is shown to markedly outperform existing approaches.","PeriodicalId":37526,"journal":{"name":"Journal of Computational Dynamics","volume":"75 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77335582","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

Rotation invariant patterns for a nonlinear Laplace-Beltrami equation: A Taylor-Chebyshev series approach 非线性Laplace-Beltrami方程的旋转不变模式:泰勒-切比雪夫级数方法

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Journal of Computational Dynamics Pub Date : 2022-01-01 DOI: 10.3934/jcd.2022005

J. B. Berg, Gabriel William Duchesne, J. Lessard

{"title":"Rotation invariant patterns for a nonlinear Laplace-Beltrami equation: A Taylor-Chebyshev series approach","authors":"J. B. Berg, Gabriel William Duchesne, J. Lessard","doi":"10.3934/jcd.2022005","DOIUrl":"https://doi.org/10.3934/jcd.2022005","url":null,"abstract":"<p style='text-indent:20px;'>In this paper, we introduce a rigorous computational approach to prove existence of rotation invariant patterns for a nonlinear Laplace-Beltrami equation posed on the 2-sphere. After changing to spherical coordinates, the problem becomes a singular second order boundary value problem (BVP) on the interval <inline-formula><tex-math id=\"M1\">begin{document}$ (0,frac{pi}{2}] $end{document}</tex-math></inline-formula> with a <i>removable</i> singularity at zero. The singularity is removed by solving the equation with Taylor series on <inline-formula><tex-math id=\"M2\">begin{document}$ (0,delta] $end{document}</tex-math></inline-formula> (with <inline-formula><tex-math id=\"M3\">begin{document}$ delta $end{document}</tex-math></inline-formula> small) while a Chebyshev series expansion is used to solve the problem on <inline-formula><tex-math id=\"M4\">begin{document}$ [delta,frac{pi}{2}] $end{document}</tex-math></inline-formula>. The two setups are incorporated in a larger zero-finding problem of the form <inline-formula><tex-math id=\"M5\">begin{document}$ F(a) = 0 $end{document}</tex-math></inline-formula> with <inline-formula><tex-math id=\"M6\">begin{document}$ a $end{document}</tex-math></inline-formula> containing the coefficients of the Taylor and Chebyshev series. The problem <inline-formula><tex-math id=\"M7\">begin{document}$ F = 0 $end{document}</tex-math></inline-formula> is solved rigorously using a Newton-Kantorovich argument.</p>","PeriodicalId":37526,"journal":{"name":"Journal of Computational Dynamics","volume":"97 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89109291","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 2