首页 > 最新文献

SIAM Journal on Applied Dynamical Systems最新文献

英文 中文
Computing Connection Matrices via Persistence-Like Reductions 通过类持久性还原计算连接矩阵
IF 2.1 4区 数学 Q2 MATHEMATICS, APPLIED Pub Date : 2024-01-04 DOI: 10.1137/23m1562469
Tamal K. Dey, Michał Lipiński, Marian Mrozek, Ryan Slechta
SIAM Journal on Applied Dynamical Systems, Volume 23, Issue 1, Page 81-97, March 2024.
Abstract. Connection matrices are a generalization of Morse boundary operators from the classical Morse theory for gradient vector fields. Developing an efficient computational framework for connection matrices is particularly important in the context of a rapidly growing data science that requires new mathematical tools for discrete data. Toward this goal, the classical theory for connection matrices has been adapted to combinatorial frameworks that facilitate computation. We develop an efficient persistence-like algorithm to compute a connection matrix from a given combinatorial (multi) vector field on a simplicial complex. This algorithm requires a single pass, improving upon a known algorithm that runs an implicit recursion executing two passes at each level. Overall, the new algorithm is more simple, direct, and efficient than the state-of-the-art. Because of the algorithm’s similarity to the persistence algorithm, one may take advantage of various software optimizations from topological data analysis.
SIAM 应用动力系统期刊》第 23 卷第 1 期第 81-97 页,2024 年 3 月。 摘要连接矩阵是梯度向量场经典莫尔斯理论中莫尔斯边界算子的广义化。在数据科学迅速发展的背景下,开发一个高效的连接矩阵计算框架尤为重要,因为数据科学需要新的数学工具来处理离散数据。为了实现这一目标,我们将连接矩阵的经典理论改编成了便于计算的组合框架。我们开发了一种高效的类似持久性的算法,可以从给定的组合(多)向量场计算简单复数上的连接矩阵。这种算法只需一次传递,改进了一种已知算法,这种算法运行隐式递归,每级执行两次传递。总体而言,新算法比最先进的算法更加简单、直接和高效。由于该算法与持久性算法相似,因此可以利用拓扑数据分析中的各种软件优化。
{"title":"Computing Connection Matrices via Persistence-Like Reductions","authors":"Tamal K. Dey, Michał Lipiński, Marian Mrozek, Ryan Slechta","doi":"10.1137/23m1562469","DOIUrl":"https://doi.org/10.1137/23m1562469","url":null,"abstract":"SIAM Journal on Applied Dynamical Systems, Volume 23, Issue 1, Page 81-97, March 2024. <br/> Abstract. Connection matrices are a generalization of Morse boundary operators from the classical Morse theory for gradient vector fields. Developing an efficient computational framework for connection matrices is particularly important in the context of a rapidly growing data science that requires new mathematical tools for discrete data. Toward this goal, the classical theory for connection matrices has been adapted to combinatorial frameworks that facilitate computation. We develop an efficient persistence-like algorithm to compute a connection matrix from a given combinatorial (multi) vector field on a simplicial complex. This algorithm requires a single pass, improving upon a known algorithm that runs an implicit recursion executing two passes at each level. Overall, the new algorithm is more simple, direct, and efficient than the state-of-the-art. Because of the algorithm’s similarity to the persistence algorithm, one may take advantage of various software optimizations from topological data analysis.","PeriodicalId":49534,"journal":{"name":"SIAM Journal on Applied Dynamical Systems","volume":"7 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139102951","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Spreading and Structural Balance on Signed Networks 签名网络的传播和结构平衡
IF 2.1 4区 数学 Q2 MATHEMATICS, APPLIED Pub Date : 2024-01-04 DOI: 10.1137/22m1542325
Yu Tian, Renaud Lambiotte
SIAM Journal on Applied Dynamical Systems, Volume 23, Issue 1, Page 50-80, March 2024.
Abstract. Two competing types of interactions often play an important part in shaping system behavior, such as activatory and inhibitory functions in biological systems. Hence, signed networks, where each connection can be either positive or negative, have become popular models over recent years. However, the primary focus of the literature is on the unweighted and structurally balanced ones, where all cycles have an even number of negative edges. Hence here, we first introduce a classification of signed networks into balanced, antibalanced, or strictly unbalanced ones, and then characterize each type of signed networks in terms of the spectral properties of the signed weighted adjacency matrix. In particular, we show that the spectral radius of the matrix with signs is smaller than that without if and only if the signed network is strictly unbalanced. These properties are important to understand the dynamics on signed networks, both linear and nonlinear ones. Specifically, we find consistent patterns in a linear and a nonlinear dynamics theoretically, depending on their type of balance. We also propose two measures to further characterize strictly unbalanced networks, motivated by perturbation theory. Finally, we numerically verify these properties through experiments on both synthetic and real networks.
SIAM 应用动力系统期刊》,第 23 卷第 1 期,第 50-80 页,2024 年 3 月。 摘要两种相互竞争的相互作用类型通常在塑造系统行为方面发挥重要作用,例如生物系统中的激活和抑制功能。因此,每个连接可以是正连接也可以是负连接的有符号网络成为近年来流行的模型。然而,文献的主要关注点是无权重和结构平衡的网络,即所有循环都有偶数条负边。因此,在这里,我们首先将有符号网络划分为平衡网络、反平衡网络和严格不平衡网络,然后根据有符号加权邻接矩阵的谱特性来描述每种类型的有符号网络。我们特别指出,如果且仅如果有符号网络是严格不平衡的,则有符号矩阵的谱半径小于无符号矩阵的谱半径。这些特性对于理解有符号网络的线性和非线性动态都非常重要。具体来说,我们发现线性动力学和非线性动力学在理论上存在一致的模式,这取决于它们的平衡类型。我们还根据扰动理论,提出了进一步描述严格不平衡网络特征的两种方法。最后,我们通过对合成网络和真实网络的实验,对这些特性进行了数值验证。
{"title":"Spreading and Structural Balance on Signed Networks","authors":"Yu Tian, Renaud Lambiotte","doi":"10.1137/22m1542325","DOIUrl":"https://doi.org/10.1137/22m1542325","url":null,"abstract":"SIAM Journal on Applied Dynamical Systems, Volume 23, Issue 1, Page 50-80, March 2024. <br/> Abstract. Two competing types of interactions often play an important part in shaping system behavior, such as activatory and inhibitory functions in biological systems. Hence, signed networks, where each connection can be either positive or negative, have become popular models over recent years. However, the primary focus of the literature is on the unweighted and structurally balanced ones, where all cycles have an even number of negative edges. Hence here, we first introduce a classification of signed networks into balanced, antibalanced, or strictly unbalanced ones, and then characterize each type of signed networks in terms of the spectral properties of the signed weighted adjacency matrix. In particular, we show that the spectral radius of the matrix with signs is smaller than that without if and only if the signed network is strictly unbalanced. These properties are important to understand the dynamics on signed networks, both linear and nonlinear ones. Specifically, we find consistent patterns in a linear and a nonlinear dynamics theoretically, depending on their type of balance. We also propose two measures to further characterize strictly unbalanced networks, motivated by perturbation theory. Finally, we numerically verify these properties through experiments on both synthetic and real networks.","PeriodicalId":49534,"journal":{"name":"SIAM Journal on Applied Dynamical Systems","volume":"23 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139102950","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Effects of Delay on the HKB Model of Human Motor Coordination 延迟对人类运动协调 HKB 模型的影响
IF 2.1 4区 数学 Q2 MATHEMATICS, APPLIED Pub Date : 2024-01-03 DOI: 10.1137/22m1531518
L. I. Allen, T. G. Molnár, Z. Dombóvári, S. J. Hogan
SIAM Journal on Applied Dynamical Systems, Volume 23, Issue 1, Page 1-25, March 2024.
Abstract. In this paper, we analyze the celebrated Haken–Kelso–Bunz model, describing the dynamics of bimanual coordination, in the presence of delay. We study the linear dynamics, stability, nonlinear behavior, and bifurcations of this model by both theoretical and numerical analysis. We calculate in-phase and antiphase limit cycles as well as quasi-periodic solutions via double Hopf bifurcation analysis and center manifold reduction. Moreover, we uncover further details on the global dynamic behavior by numerical continuation, including the occurrence of limit cycles in phase quadrature and 1-1 locking of quasi-periodic solutions.
SIAM 应用动力系统期刊》第 23 卷第 1 期第 1-25 页,2024 年 3 月。 摘要在本文中,我们分析了著名的 Haken-Kelso-Bunz 模型,该模型描述了存在延迟的双臂协调动力学。我们通过理论和数值分析研究了该模型的线性动力学、稳定性、非线性行为和分岔。我们通过双霍普夫分岔分析和中心流形还原计算了同相和反相极限循环以及准周期解。此外,我们还通过数值延续揭示了全局动态行为的更多细节,包括相位正交极限循环的出现和准周期解的 1-1 锁定。
{"title":"The Effects of Delay on the HKB Model of Human Motor Coordination","authors":"L. I. Allen, T. G. Molnár, Z. Dombóvári, S. J. Hogan","doi":"10.1137/22m1531518","DOIUrl":"https://doi.org/10.1137/22m1531518","url":null,"abstract":"SIAM Journal on Applied Dynamical Systems, Volume 23, Issue 1, Page 1-25, March 2024. <br/> Abstract. In this paper, we analyze the celebrated Haken–Kelso–Bunz model, describing the dynamics of bimanual coordination, in the presence of delay. We study the linear dynamics, stability, nonlinear behavior, and bifurcations of this model by both theoretical and numerical analysis. We calculate in-phase and antiphase limit cycles as well as quasi-periodic solutions via double Hopf bifurcation analysis and center manifold reduction. Moreover, we uncover further details on the global dynamic behavior by numerical continuation, including the occurrence of limit cycles in phase quadrature and 1-1 locking of quasi-periodic solutions.","PeriodicalId":49534,"journal":{"name":"SIAM Journal on Applied Dynamical Systems","volume":"1 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139093876","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Truncation of Contact Defects in Reaction-Diffusion Systems 反应-扩散系统中接触缺陷的截断
IF 2.1 4区 数学 Q2 MATHEMATICS, APPLIED Pub Date : 2024-01-03 DOI: 10.1137/23m1546257
Milen Ivanov, Björn Sandstede
SIAM Journal on Applied Dynamical Systems, Volume 23, Issue 1, Page 26-49, March 2024.
Abstract. Contact defects are time-periodic patterns in one space dimension that resemble spatially homogeneous oscillations with a defect embedded in their core region. For theoretical and numerical purposes, it is important to understand whether these defects persist when the domain is truncated to large spatial intervals, supplemented by appropriate boundary conditions. The present work shows that truncated contact defects exist and are unique on sufficiently large spatial intervals.
SIAM 应用动力系统期刊》,第 23 卷第 1 期,第 26-49 页,2024 年 3 月。 摘要接触缺陷是在一个空间维度上的时间周期性模式,类似于在其核心区域嵌入缺陷的空间均匀振荡。为了理论和数值目的,了解当域被截断到大的空间间隔并辅以适当的边界条件时,这些缺陷是否持续存在非常重要。本研究表明,截断接触缺陷是存在的,而且在足够大的空间间隔上是唯一的。
{"title":"Truncation of Contact Defects in Reaction-Diffusion Systems","authors":"Milen Ivanov, Björn Sandstede","doi":"10.1137/23m1546257","DOIUrl":"https://doi.org/10.1137/23m1546257","url":null,"abstract":"SIAM Journal on Applied Dynamical Systems, Volume 23, Issue 1, Page 26-49, March 2024. <br/> Abstract. Contact defects are time-periodic patterns in one space dimension that resemble spatially homogeneous oscillations with a defect embedded in their core region. For theoretical and numerical purposes, it is important to understand whether these defects persist when the domain is truncated to large spatial intervals, supplemented by appropriate boundary conditions. The present work shows that truncated contact defects exist and are unique on sufficiently large spatial intervals.","PeriodicalId":49534,"journal":{"name":"SIAM Journal on Applied Dynamical Systems","volume":"22 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139093581","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Stability of the Nonwandering Set in the Region of Attraction Boundary under Perturbations with Application to Vulnerability Assessment 吸引边界区域非游走集在扰动下的稳定性及在脆弱性评估中的应用
IF 2.1 4区 数学 Q2 MATHEMATICS, APPLIED Pub Date : 2023-12-07 DOI: 10.1137/23m155582x
Michael W. Fisher, Ian A. Hiskens
SIAM Journal on Applied Dynamical Systems, Volume 22, Issue 4, Page 3390-3430, December 2023.
Abstract. For many engineered systems it is important to assess vulnerability to potential disturbances in order to ensure reliable operation. Whether the system will recover from a particular finite-time disturbance to a desired stable equilibrium point depends on uncertain and time-varying system parameter values. Therefore, it is valuable to determine, for specific fixed disturbances, the margins for safe operation: the smallest change in parameter values that would cause the system to become vulnerable to the disturbance. The natural setting for this problem is a parameter-dependent vector field with a family of stable equilibria and a parameter-dependent initial condition representing the disturbance. The system recovers for a particular parameter value if its initial condition lies within the region of attraction of the desired stable equilibrium point. Prior work has developed algorithms for numerically computing the margins for safe operation. However, the theoretical guarantees provided for these methods require a very restrictive assumption: that the nonwandering set in the region of attraction boundary is stable under perturbations to the vector field. This assumption is generally intractable to verify, so feasibility of the above algorithms cannot be determined in advance, and even when these algorithms do converge their convergence to the correct values cannot be guaranteed. Thus, this assumption limits the effective application of these algorithms in practice. This work relaxes this restrictive assumption while still obtaining similar results under weaker assumptions, thereby guaranteeing effectiveness of these algorithms. For the setting under consideration, it is shown for vector fields on compact Riemannian manifolds that the restrictive assumption follows immediately and does not need to be independently verified. A motivating example shows that this is not the case for vector fields on Euclidean space, but in this setting it is shown that the restrictive assumption can still be relaxed provided there exist a neighborhood of infinity with suitable properties and some additional generic assumptions. These results are then used to provide theoretical guarantees for the numerical algorithms discussed above under far weaker assumptions.
SIAM 应用动力系统期刊》,第 22 卷第 4 期,第 3390-3430 页,2023 年 12 月。 摘要对于许多工程系统来说,评估对潜在干扰的脆弱性以确保可靠运行非常重要。系统能否从特定的有限时间干扰中恢复到所需的稳定平衡点,取决于不确定的时变系统参数值。因此,对于特定的固定扰动,确定安全运行的裕度是很有价值的:即会导致系统易受扰动影响的参数值的最小变化。这一问题的自然背景是一个与参数相关的矢量场,该矢量场具有一系列稳定的平衡点和一个代表干扰的与参数相关的初始条件。如果系统的初始条件位于所需的稳定平衡点的吸引区域内,则系统会在特定参数值下恢复。之前的工作已经开发出了数值计算安全运行裕度的算法。然而,这些方法的理论保证需要一个限制性很强的假设:在矢量场的扰动下,吸引力边界区域内的非漂移集是稳定的。这一假设通常难以验证,因此无法事先确定上述算法的可行性,即使这些算法确实收敛,也无法保证其收敛到正确的值。因此,这一假设限制了这些算法在实践中的有效应用。这项工作放宽了这一限制性假设,同时在较弱的假设条件下仍能得到类似的结果,从而保证了这些算法的有效性。对于所考虑的环境,对于紧凑黎曼流形上的向量场,研究表明限制性假设是直接得出的,无需独立验证。一个激励性的例子表明,欧几里得空间上的向量场并非如此,但在这种情况下,只要存在具有适当性质的无穷邻域和一些额外的一般假设,限制性假设仍然可以放宽。然后,这些结果被用来为上文讨论的数值算法提供理论保证,而这些算法是在弱得多的假设条件下进行的。
{"title":"Stability of the Nonwandering Set in the Region of Attraction Boundary under Perturbations with Application to Vulnerability Assessment","authors":"Michael W. Fisher, Ian A. Hiskens","doi":"10.1137/23m155582x","DOIUrl":"https://doi.org/10.1137/23m155582x","url":null,"abstract":"SIAM Journal on Applied Dynamical Systems, Volume 22, Issue 4, Page 3390-3430, December 2023. <br/> Abstract. For many engineered systems it is important to assess vulnerability to potential disturbances in order to ensure reliable operation. Whether the system will recover from a particular finite-time disturbance to a desired stable equilibrium point depends on uncertain and time-varying system parameter values. Therefore, it is valuable to determine, for specific fixed disturbances, the margins for safe operation: the smallest change in parameter values that would cause the system to become vulnerable to the disturbance. The natural setting for this problem is a parameter-dependent vector field with a family of stable equilibria and a parameter-dependent initial condition representing the disturbance. The system recovers for a particular parameter value if its initial condition lies within the region of attraction of the desired stable equilibrium point. Prior work has developed algorithms for numerically computing the margins for safe operation. However, the theoretical guarantees provided for these methods require a very restrictive assumption: that the nonwandering set in the region of attraction boundary is stable under perturbations to the vector field. This assumption is generally intractable to verify, so feasibility of the above algorithms cannot be determined in advance, and even when these algorithms do converge their convergence to the correct values cannot be guaranteed. Thus, this assumption limits the effective application of these algorithms in practice. This work relaxes this restrictive assumption while still obtaining similar results under weaker assumptions, thereby guaranteeing effectiveness of these algorithms. For the setting under consideration, it is shown for vector fields on compact Riemannian manifolds that the restrictive assumption follows immediately and does not need to be independently verified. A motivating example shows that this is not the case for vector fields on Euclidean space, but in this setting it is shown that the restrictive assumption can still be relaxed provided there exist a neighborhood of infinity with suitable properties and some additional generic assumptions. These results are then used to provide theoretical guarantees for the numerical algorithms discussed above under far weaker assumptions.","PeriodicalId":49534,"journal":{"name":"SIAM Journal on Applied Dynamical Systems","volume":"12 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2023-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138552725","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Bifurcation of Limit Cycles from Boundary Equilibria in Impacting Hybrid Systems 撞击混合系统中边界平衡的极限循环分岔
IF 2.1 4区 数学 Q2 MATHEMATICS, APPLIED Pub Date : 2023-12-06 DOI: 10.1137/23m1552292
Hong Tang, Alan Champneys
SIAM Journal on Applied Dynamical Systems, Volume 22, Issue 4, Page 3320-3357, December 2023.
Abstract. A semianalytical method is derived for finding the existence and stability of single-impact periodic orbits born in a boundary equilibrium bifurcation in a general [math]-dimensional impacting hybrid system. Known results are reproduced for planar systems and general formulae derived for three-dimensional (3D) systems. A numerical implementation of the method is illustrated for several 3D examples and for an 8D wing-flap model that shows coexistence of attractors. It is shown how the method can easily be embedded within numerical continuation, and some remarks are made about necessary and sufficient conditions in arbitrary dimensional systems.
SIAM 应用动力系统期刊》,第 22 卷第 4 期,第 3320-3357 页,2023 年 12 月。 摘要。推导了一种半解析方法,用于求解一般[数学]维碰撞混合系统中边界平衡分岔所产生的单碰撞周期轨道的存在性和稳定性。已知结果用于平面系统,一般公式用于三维(3D)系统。针对几个三维实例和一个显示吸引子共存的 8D 翼瓣模型,对该方法的数值实现进行了说明。图中展示了如何将该方法轻松嵌入数值延续中,并对任意维度系统中的必要条件和充分条件做了一些说明。
{"title":"Bifurcation of Limit Cycles from Boundary Equilibria in Impacting Hybrid Systems","authors":"Hong Tang, Alan Champneys","doi":"10.1137/23m1552292","DOIUrl":"https://doi.org/10.1137/23m1552292","url":null,"abstract":"SIAM Journal on Applied Dynamical Systems, Volume 22, Issue 4, Page 3320-3357, December 2023. <br/> Abstract. A semianalytical method is derived for finding the existence and stability of single-impact periodic orbits born in a boundary equilibrium bifurcation in a general [math]-dimensional impacting hybrid system. Known results are reproduced for planar systems and general formulae derived for three-dimensional (3D) systems. A numerical implementation of the method is illustrated for several 3D examples and for an 8D wing-flap model that shows coexistence of attractors. It is shown how the method can easily be embedded within numerical continuation, and some remarks are made about necessary and sufficient conditions in arbitrary dimensional systems.","PeriodicalId":49534,"journal":{"name":"SIAM Journal on Applied Dynamical Systems","volume":"35 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2023-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138545624","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Rocking Can: A Reduced Equation of Motion and a Matched Asymptotic Solution 摇摆罐简化运动方程和匹配渐近解
IF 2.1 4区 数学 Q2 MATHEMATICS, APPLIED Pub Date : 2023-12-06 DOI: 10.1137/23m1551031
B. W. Collins, C. L. Hall, S. J. Hogan
SIAM Journal on Applied Dynamical Systems, Volume 22, Issue 4, Page 3358-3389, December 2023.
Abstract. The rocking can problem [M. Srinivasan and A. Ruina, Phys. Rev. E, 78 (2008), 066609] consists of an empty drinks can standing upright on a horizontal plane which, when tipped back to a single contact point and released, rocks down towards the flat and level state. At the bottom of the motion, the contact point moves quickly around the rim of the can. The can then rises up again, having rotated through some finite angle of turn [math]. We recast the problem as a second order ODE and find a Frobenius solution. We then use this Frobenius solution to derive a reduced equation of motion. The rocking can exhibits two distinct phenomena: behavior very similar to an inverted pendulum, and dynamics with the angle of turn. This distinction allows us to use matched asymptotic expansions to derive a uniformly valid solution that is in excellent agreement with numerical calculations of the reduced equation of motion. The solution of the inner problem was used to investigate of the angle of turn phenomenon. We also examine the motion of the contact locus [math] and see a range of different trajectories, from circular to petaloid motion and even cusp-like behavior. Finally, we obtain an approximate lower bound for the required coefficient of friction to avoid slip.
SIAM 应用动力系统期刊》,第 22 卷第 4 期,第 3358-3389 页,2023 年 12 月。 摘要。摇罐问题 [M. Srinivasan and A. Ruina, Phys. Rev. E, 78 (2008), 066609] 包含一个直立在水平面上的空饮料罐。在运动的底部,接触点围绕罐子边缘快速移动。然后,罐子再次上升,旋转了某个有限的角度[数学]。我们将问题重塑为一个二阶 ODE,并找到一个 Frobenius 解。然后,我们利用这个弗罗贝尼斯解推导出一个简化的运动方程。摇摆可以表现出两种截然不同的现象:与倒立摆非常相似的行为,以及随转角变化的动力学。这种区别使我们能够使用匹配的渐近展开求出统一有效的解,该解与简化运动方程的数值计算结果非常吻合。内部问题的解被用来研究转角现象。我们还研究了接触点的运动[math],看到了一系列不同的轨迹,从圆周运动到花瓣运动,甚至是类似尖顶的行为。最后,我们得到了避免滑移所需的摩擦系数的近似下限。
{"title":"The Rocking Can: A Reduced Equation of Motion and a Matched Asymptotic Solution","authors":"B. W. Collins, C. L. Hall, S. J. Hogan","doi":"10.1137/23m1551031","DOIUrl":"https://doi.org/10.1137/23m1551031","url":null,"abstract":"SIAM Journal on Applied Dynamical Systems, Volume 22, Issue 4, Page 3358-3389, December 2023. <br/> Abstract. The rocking can problem [M. Srinivasan and A. Ruina, Phys. Rev. E, 78 (2008), 066609] consists of an empty drinks can standing upright on a horizontal plane which, when tipped back to a single contact point and released, rocks down towards the flat and level state. At the bottom of the motion, the contact point moves quickly around the rim of the can. The can then rises up again, having rotated through some finite angle of turn [math]. We recast the problem as a second order ODE and find a Frobenius solution. We then use this Frobenius solution to derive a reduced equation of motion. The rocking can exhibits two distinct phenomena: behavior very similar to an inverted pendulum, and dynamics with the angle of turn. This distinction allows us to use matched asymptotic expansions to derive a uniformly valid solution that is in excellent agreement with numerical calculations of the reduced equation of motion. The solution of the inner problem was used to investigate of the angle of turn phenomenon. We also examine the motion of the contact locus [math] and see a range of different trajectories, from circular to petaloid motion and even cusp-like behavior. Finally, we obtain an approximate lower bound for the required coefficient of friction to avoid slip.","PeriodicalId":49534,"journal":{"name":"SIAM Journal on Applied Dynamical Systems","volume":"133 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2023-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138545842","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Symplectic Methods in the Numerical Search of Orbits in Real-Life Planetary Systems 现实行星系统轨道数值搜索中的辛方法
IF 2.1 4区 数学 Q2 MATHEMATICS, APPLIED Pub Date : 2023-12-05 DOI: 10.1137/22m1500459
Urs Frauenfelder, Dayung Koh, Agustin Moreno
SIAM Journal on Applied Dynamical Systems, Volume 22, Issue 4, Page 3284-3319, December 2023.
Abstract. The intention of this article is to illustrate the use of methods from symplectic geometry for practical purposes. Our intended audience is scientists interested in orbits of Hamiltonian systems (e.g., the three-body problem). The main directions pursued in this article are as follows: (1) given two periodic orbits, decide when they can be connected by a regular family of periodic orbits; (2) use numerical invariants from Floer theory which help predict the existence of orbits in the presence of a bifurcation; (3) attach a sign [math] to each elliptic or hyperbolic Floquet multiplier of a closed symmetric orbit, which generalizes the classical Krein–Moser sign to also include the hyperbolic case; and (4) do all of the above in a visual, easily implementable, and resource-efficient way. The mathematical framework is provided by the first and third authors in [U. Frauenfelder and A. Moreno, J. Symplectic Geom., to appear], where, as it turns out, the “Broucke stability diagram” [R. Broucke, AIAA J., 7 (1969), pp. 1003–1009] was rediscovered, but further refined with the above signs and algebraically reformulated in terms of quotients of the symplectic group. The advantage of the framework is that it applies to the study of closed orbits of an arbitrary Hamiltonian system. We will carry out numerical work based on the cell-mapping method as described in [D. Koh, R. L. Anderson, and I. Bermejo-Moreno, J. Astronautical Sci., 68 (2021), pp. 172–196] for the Jupiter-Europa and Saturn-Enceladus systems. These are currently systems of interest, falling in the agenda of space agencies like NASA, as these icy moons are considered candidates for harboring conditions suitable for extraterrestrial life.
应用动力系统学报,第22卷,第4期,3284-3319页,2023年12月。摘要。本文的目的是说明辛几何方法的实际用途。我们的目标读者是对哈密顿系统的轨道(例如,三体问题)感兴趣的科学家。本文的主要研究方向如下:(1)给定两个周期轨道,确定它们何时可以由一个规则的周期轨道族连接起来;(2)利用Floer理论中的数值不变量来预测存在分岔时轨道的存在性;(3)在闭对称轨道的每个椭圆或双曲Floquet乘法器上附加一个符号[math],将经典的klein - moser符号推广到双曲情况;(4)以可视化、易于实现和资源高效的方式完成上述所有工作。数学框架是由[美国]的第一和第三作者提供的。莫雷诺,李建平。,在那里,事实证明,“布鲁克稳定性图”[R。Broucke, AIAA J., 7 (1969), pp. 1003-1009]被重新发现,但进一步改进了上述符号,并用辛群的商进行了代数上的重新表述。该框架的优点是它适用于研究任意哈密顿系统的封闭轨道。我们将根据[D]中描述的细胞映射方法开展数值工作。Koh, R. L. Anderson, I. Bermejo-Moreno, J.宇航科学。木星-木卫二和土星-土卫二系统,68(2021),第172-196页。这些都是目前人们感兴趣的系统,被列入了美国宇航局等太空机构的议程,因为这些冰冷的卫星被认为是适合外星生命生存的候选者。
{"title":"Symplectic Methods in the Numerical Search of Orbits in Real-Life Planetary Systems","authors":"Urs Frauenfelder, Dayung Koh, Agustin Moreno","doi":"10.1137/22m1500459","DOIUrl":"https://doi.org/10.1137/22m1500459","url":null,"abstract":"SIAM Journal on Applied Dynamical Systems, Volume 22, Issue 4, Page 3284-3319, December 2023. <br/> Abstract. The intention of this article is to illustrate the use of methods from symplectic geometry for practical purposes. Our intended audience is scientists interested in orbits of Hamiltonian systems (e.g., the three-body problem). The main directions pursued in this article are as follows: (1) given two periodic orbits, decide when they can be connected by a regular family of periodic orbits; (2) use numerical invariants from Floer theory which help predict the existence of orbits in the presence of a bifurcation; (3) attach a sign [math] to each elliptic or hyperbolic Floquet multiplier of a closed symmetric orbit, which generalizes the classical Krein–Moser sign to also include the hyperbolic case; and (4) do all of the above in a visual, easily implementable, and resource-efficient way. The mathematical framework is provided by the first and third authors in [U. Frauenfelder and A. Moreno, J. Symplectic Geom., to appear], where, as it turns out, the “Broucke stability diagram” [R. Broucke, AIAA J., 7 (1969), pp. 1003–1009] was rediscovered, but further refined with the above signs and algebraically reformulated in terms of quotients of the symplectic group. The advantage of the framework is that it applies to the study of closed orbits of an arbitrary Hamiltonian system. We will carry out numerical work based on the cell-mapping method as described in [D. Koh, R. L. Anderson, and I. Bermejo-Moreno, J. Astronautical Sci., 68 (2021), pp. 172–196] for the Jupiter-Europa and Saturn-Enceladus systems. These are currently systems of interest, falling in the agenda of space agencies like NASA, as these icy moons are considered candidates for harboring conditions suitable for extraterrestrial life.","PeriodicalId":49534,"journal":{"name":"SIAM Journal on Applied Dynamical Systems","volume":"46 ","pages":""},"PeriodicalIF":2.1,"publicationDate":"2023-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138505527","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Kuramoto Networks with Infinitely Many Stable Equilibria 具有无穷多稳定平衡点的Kuramoto网络
IF 2.1 4区 数学 Q2 MATHEMATICS, APPLIED Pub Date : 2023-11-30 DOI: 10.1137/23m155400x
Davide Sclosa
SIAM Journal on Applied Dynamical Systems, Volume 22, Issue 4, Page 3267-3283, December 2023.
Abstract. We prove that the Kuramoto model on a graph can contain infinitely many nonequivalent stable equilibria. More precisely, we prove that for every [math] there is a connected graph such that the set of stable equilibria contains a manifold of dimension [math]. In particular, we solve a conjecture of Delabays, Coletta, and Jacquod about the number of equilibria on planar graphs. Our results are based on the analysis of balanced configurations, which correspond to equilateral polygon linkages in topology. In order to analyze the stability of manifolds of equilibria we apply topological bifurcation theory.
应用动力系统学报,vol . 22, Issue 4, Page 3267-3283, December 2023。摘要。证明了图上的Kuramoto模型可以包含无穷多个非等价稳定平衡点。更准确地说,我们证明了对于每一个[数学]存在一个连通图,使得稳定均衡集包含一个维数[数学]的流形。特别地,我们解决了Delabays, Coletta和Jacquod关于平面图上平衡点数目的猜想。我们的结果是基于平衡构型的分析,它对应于拓扑中的等边多边形连杆。为了分析平衡流形的稳定性,我们应用了拓扑分岔理论。
{"title":"Kuramoto Networks with Infinitely Many Stable Equilibria","authors":"Davide Sclosa","doi":"10.1137/23m155400x","DOIUrl":"https://doi.org/10.1137/23m155400x","url":null,"abstract":"SIAM Journal on Applied Dynamical Systems, Volume 22, Issue 4, Page 3267-3283, December 2023. <br/> Abstract. We prove that the Kuramoto model on a graph can contain infinitely many nonequivalent stable equilibria. More precisely, we prove that for every [math] there is a connected graph such that the set of stable equilibria contains a manifold of dimension [math]. In particular, we solve a conjecture of Delabays, Coletta, and Jacquod about the number of equilibria on planar graphs. Our results are based on the analysis of balanced configurations, which correspond to equilateral polygon linkages in topology. In order to analyze the stability of manifolds of equilibria we apply topological bifurcation theory.","PeriodicalId":49534,"journal":{"name":"SIAM Journal on Applied Dynamical Systems","volume":"44 11","pages":""},"PeriodicalIF":2.1,"publicationDate":"2023-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138505513","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Quantifying Different Modeling Frameworks Using Topological Data Analysis: A Case Study with Zebrafish Patterns 使用拓扑数据分析量化不同的建模框架:斑马鱼模式的案例研究
IF 2.1 4区 数学 Q2 MATHEMATICS, APPLIED Pub Date : 2023-11-29 DOI: 10.1137/22m1543082
Electa Cleveland, Angela Zhu, Björn Sandstede, Alexandria Volkening
SIAM Journal on Applied Dynamical Systems, Volume 22, Issue 4, Page 3233-3266, December 2023.
Abstract. Mathematical models come in many forms across biological applications. In the case of complex, spatial dynamics and pattern formation, stochastic models also face two main challenges: pattern data are largely qualitative, and model realizations may vary significantly. Together these issues make it difficult to relate models and empirical data—or even models and models—limiting how different approaches can be combined to offer new insights into biology. These challenges also raise mathematical questions about how models are related, since alternative approaches to the same problem—e.g., Cellular Potts models; off-lattice, agent-based models; on-lattice, cellular automaton models; and continuum approaches—treat uncertainty and implement cell behavior in different ways. To help open the door to future work on questions like these, here we adapt methods from topological data analysis and computational geometry to quantitatively relate two different models of the same biological process in a fair, comparable way. To center our work and illustrate concrete challenges, we focus on the example of zebrafish-skin pattern formation, and we relate patterns that arise from agent-based and cellular automaton models.
应用动力系统学报,第22卷,第4期,第3233-3266页,2023年12月。摘要。数学模型在生物学应用中有多种形式。在复杂的空间动态和模式形成的情况下,随机模型也面临两个主要挑战:模式数据在很大程度上是定性的,模型实现可能会有很大差异。综上所述,这些问题使得很难将模型和经验数据联系起来,甚至是模型和模型之间的联系,从而限制了不同方法的结合,从而为生物学提供新的见解。这些挑战也提出了关于模型之间如何关联的数学问题,因为同样的问题有不同的解决方法。, Cellular Potts模型;离格、基于智能体的模型;点阵、元胞自动机模型;连续方法——以不同的方式处理不确定性和实现细胞行为。为了帮助打开这类问题的未来工作之门,在这里,我们采用拓扑数据分析和计算几何的方法,以公平、可比的方式定量地联系同一生物过程的两种不同模型。为了集中我们的工作并说明具体的挑战,我们将重点放在斑马鱼皮肤模式形成的例子上,并将基于主体和元胞自动机模型产生的模式联系起来。
{"title":"Quantifying Different Modeling Frameworks Using Topological Data Analysis: A Case Study with Zebrafish Patterns","authors":"Electa Cleveland, Angela Zhu, Björn Sandstede, Alexandria Volkening","doi":"10.1137/22m1543082","DOIUrl":"https://doi.org/10.1137/22m1543082","url":null,"abstract":"SIAM Journal on Applied Dynamical Systems, Volume 22, Issue 4, Page 3233-3266, December 2023. <br/> Abstract. Mathematical models come in many forms across biological applications. In the case of complex, spatial dynamics and pattern formation, stochastic models also face two main challenges: pattern data are largely qualitative, and model realizations may vary significantly. Together these issues make it difficult to relate models and empirical data—or even models and models—limiting how different approaches can be combined to offer new insights into biology. These challenges also raise mathematical questions about how models are related, since alternative approaches to the same problem—e.g., Cellular Potts models; off-lattice, agent-based models; on-lattice, cellular automaton models; and continuum approaches—treat uncertainty and implement cell behavior in different ways. To help open the door to future work on questions like these, here we adapt methods from topological data analysis and computational geometry to quantitatively relate two different models of the same biological process in a fair, comparable way. To center our work and illustrate concrete challenges, we focus on the example of zebrafish-skin pattern formation, and we relate patterns that arise from agent-based and cellular automaton models.","PeriodicalId":49534,"journal":{"name":"SIAM Journal on Applied Dynamical Systems","volume":"47 ","pages":""},"PeriodicalIF":2.1,"publicationDate":"2023-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138505526","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
期刊
SIAM Journal on Applied Dynamical Systems
全部 Acc. Chem. Res. ACS Applied Bio Materials ACS Appl. Electron. Mater. ACS Appl. Energy Mater. ACS Appl. Mater. Interfaces ACS Appl. Nano Mater. ACS Appl. Polym. Mater. ACS BIOMATER-SCI ENG ACS Catal. ACS Cent. Sci. ACS Chem. Biol. ACS Chemical Health & Safety ACS Chem. Neurosci. ACS Comb. Sci. ACS Earth Space Chem. ACS Energy Lett. ACS Infect. Dis. ACS Macro Lett. ACS Mater. Lett. ACS Med. Chem. Lett. ACS Nano ACS Omega ACS Photonics ACS Sens. ACS Sustainable Chem. Eng. ACS Synth. Biol. Anal. Chem. BIOCHEMISTRY-US Bioconjugate Chem. BIOMACROMOLECULES Chem. Res. Toxicol. Chem. Rev. Chem. Mater. CRYST GROWTH DES ENERG FUEL Environ. Sci. Technol. Environ. Sci. Technol. Lett. Eur. J. Inorg. Chem. IND ENG CHEM RES Inorg. Chem. J. Agric. Food. Chem. J. Chem. Eng. Data J. Chem. Educ. J. Chem. Inf. Model. J. Chem. Theory Comput. J. Med. Chem. J. Nat. Prod. J PROTEOME RES J. Am. Chem. Soc. LANGMUIR MACROMOLECULES Mol. Pharmaceutics Nano Lett. Org. Lett. ORG PROCESS RES DEV ORGANOMETALLICS J. Org. Chem. J. Phys. Chem. J. Phys. Chem. A J. Phys. Chem. B J. Phys. Chem. C J. Phys. Chem. Lett. Analyst Anal. Methods Biomater. Sci. Catal. Sci. Technol. Chem. Commun. Chem. Soc. Rev. CHEM EDUC RES PRACT CRYSTENGCOMM Dalton Trans. Energy Environ. Sci. ENVIRON SCI-NANO ENVIRON SCI-PROC IMP ENVIRON SCI-WAT RES Faraday Discuss. Food Funct. Green Chem. Inorg. Chem. Front. Integr. Biol. J. Anal. At. Spectrom. J. Mater. Chem. A J. Mater. Chem. B J. Mater. Chem. C Lab Chip Mater. Chem. Front. Mater. Horiz. MEDCHEMCOMM Metallomics Mol. Biosyst. Mol. Syst. Des. Eng. Nanoscale Nanoscale Horiz. Nat. Prod. Rep. New J. Chem. Org. Biomol. Chem. Org. Chem. Front. PHOTOCH PHOTOBIO SCI PCCP Polym. Chem.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1