SIAM Journal on Applied Dynamical Systems最新文献_第6页

A Computational Approach to Polynomial Conservation Laws 多项式守恒定律的计算方法

IF 2.1 4区数学

SIAM Journal on Applied Dynamical Systems Pub Date : 2024-03-12 DOI: 10.1137/22m1544014

Aurélien Desoeuvres, Alexandru Iosif, Christoph Lüders, Ovidiu Radulescu, Hamid Rahkooy, Matthias Seiß, Thomas Sturm

{"title":"A Computational Approach to Polynomial Conservation Laws","authors":"Aurélien Desoeuvres, Alexandru Iosif, Christoph Lüders, Ovidiu Radulescu, Hamid Rahkooy, Matthias Seiß, Thomas Sturm","doi":"10.1137/22m1544014","DOIUrl":"https://doi.org/10.1137/22m1544014","url":null,"abstract":"SIAM Journal on Applied Dynamical Systems, Volume 23, Issue 1, Page 813-854, March 2024. Abstract.For polynomial ODE models, we introduce and discuss the concepts of exact and approximate conservation laws, which are the first integrals of the full and truncated sets of ODEs. For fast-slow systems, truncated ODEs describe the fast dynamics. We define compatibility classes as subsets of the state space, obtained by equating the conservation laws to constants. A set of conservation laws is complete when the corresponding compatibility classes contain a finite number of steady states. Complete sets of conservation laws can be used for model order reduction and for studying the multistationarity of the model. We provide algorithmic methods for computing linear, monomial, and polynomial conservation laws of polynomial ODE models and for testing their completeness. The resulting conservation laws and their completeness are either independent or dependent on the parameters. In the latter case, we provide parametric case distinctions. In particular, we propose a new method to compute polynomial conservation laws by comprehensive Gröbner systems and syzygies.","PeriodicalId":49534,"journal":{"name":"SIAM Journal on Applied Dynamical Systems","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140116744","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

Preserving Bifurcations through Moment Closures 通过时刻闭合保护分岔

IF 2.1 4区数学

SIAM Journal on Applied Dynamical Systems Pub Date : 2024-03-12 DOI: 10.1137/23m158440x

Christian Kuehn, Jan Mölter

{"title":"Preserving Bifurcations through Moment Closures","authors":"Christian Kuehn, Jan Mölter","doi":"10.1137/23m158440x","DOIUrl":"https://doi.org/10.1137/23m158440x","url":null,"abstract":"SIAM Journal on Applied Dynamical Systems, Volume 23, Issue 1, Page 791-812, March 2024. Abstract.Moment systems arise in a wide range of contexts and applications, e.g., in network modeling of complex systems. Since moment systems consist of a high or even infinite number of coupled equations, an indispensable step in obtaining a low-dimensional representation that is amenable to further analysis is, in many cases, to select a moment closure. A moment closure consists of a set of approximations that express certain higher-order moments in terms of lower-order ones, so that applying those leads to a closed system of equations for only the lower-order moments. Closures are frequently found drawing on intuition and heuristics to come up with quantitatively good approximations. In contrast to that, we propose an alternative approach where we instead focus on closures giving rise to certain qualitative features, such as bifurcations. Importantly, this fundamental change of perspective provides one with the possibility of classifying moment closures rigorously in regard to these features. This makes the design and selection of closures more algorithmic, precise, and reliable. In this work, we carefully study the moment systems that arise in the mean-field descriptions of two widely known network dynamical systems, the SIS epidemic and the adaptive voter model. We derive conditions that any moment closure has to satisfy so that the corresponding closed systems exhibit the transcritical bifurcation that one expects in these systems coming from the stochastic particle model.","PeriodicalId":49534,"journal":{"name":"SIAM Journal on Applied Dynamical Systems","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140116732","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

Guarantees for Spontaneous Synchronization on Random Geometric Graphs 随机几何图上的自发同步保证

IF 2.1 4区数学

SIAM Journal on Applied Dynamical Systems Pub Date : 2024-03-07 DOI: 10.1137/23m1559270

Pedro Abdalla, Afonso S. Bandeira, Clara Invernizzi

引用次数: 0

Dynamics of Controllable Matter-Wave Solitons and Soliton Molecules for a Rabi-Coupled Gross–Pitaevskii Equation with Temporally and Spatially Modulated Coefficients 具有时空调制系数的 Rabi-Coupled Gross-Pitaevskii 方程的可控物质波孤子和孤子分子动力学

IF 2.1 4区数学

SIAM Journal on Applied Dynamical Systems Pub Date : 2024-02-28 DOI: 10.1137/23m155551x

Haotian Wang, Hujiang Yang, Xiankui Meng, Ye Tian, Wenjun Liu

{"title":"Dynamics of Controllable Matter-Wave Solitons and Soliton Molecules for a Rabi-Coupled Gross–Pitaevskii Equation with Temporally and Spatially Modulated Coefficients","authors":"Haotian Wang, Hujiang Yang, Xiankui Meng, Ye Tian, Wenjun Liu","doi":"10.1137/23m155551x","DOIUrl":"https://doi.org/10.1137/23m155551x","url":null,"abstract":"SIAM Journal on Applied Dynamical Systems, Volume 23, Issue 1, Page 748-778, March 2024. Abstract. This paper studies the soliton dynamics for the Rabi-coupled Gross–Pitaevskii model in multicomponent Bose–Einstein condensates. The model has variable nonlinearities and external potentials and is used to construct a complex multisoliton in an explicit form. The variable nonlinearity and external potential cause the soliton to compress and change its velocity, respectively. A new generalized similarity transformation is proposed to eliminate the [math] Rabi-coupled terms in the [math]-component model, which can make the Hirota bilinear method be applied to obtain multisoliton solutions. The bound state of the two-soliton forms the soliton molecule under velocity resonance. Asymptotic analysis can give the asymptotic expressions of each single soliton in multisoliton solutions, which can clearly give each soliton’s width, velocity, amplitude, and energy; these parameters can control multisolitons. When the solitons’ relative velocity or the solitons’ width is large, the interferogram between solitons will be observed. Numerical simulation shows that these solitons can steadily propagate. It is easy for the soliton molecule and interference dynamics to occur because of the controlled soliton. Since the coupled Gross–Pitaevskii equation describes the mechanics of matter waves in Bose–Einstein condensates, it is proved that we can observe the stable solitons and soliton molecules in Bose–Einstein condensates. The method and results presented in this paper are also common to other similar models. When observing particle multiple distributions, quantum interferometry, and interferometers, the results presented and the model in this paper can provide a reference for these applications.","PeriodicalId":49534,"journal":{"name":"SIAM Journal on Applied Dynamical Systems","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140011084","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

Wave-Pinned Patterns for Cell Polarity—A Catastrophe Theory Explanation 细胞极性的波钉模式--灾难理论的解释

IF 2.1 4区数学

SIAM Journal on Applied Dynamical Systems Pub Date : 2024-02-26 DOI: 10.1137/22m1509758

Fahad Al Saadi, Alan Champneys, Mike R. Jeffrey

{"title":"Wave-Pinned Patterns for Cell Polarity—A Catastrophe Theory Explanation","authors":"Fahad Al Saadi, Alan Champneys, Mike R. Jeffrey","doi":"10.1137/22m1509758","DOIUrl":"https://doi.org/10.1137/22m1509758","url":null,"abstract":"SIAM Journal on Applied Dynamical Systems, Volume 23, Issue 1, Page 721-747, March 2024. Abstract.A class of four-component reaction-diffusion systems are studied in one spatial dimension, with one of four specific reaction kinetics. Models of this type seek to capture the interaction between active and inactive forms of two G-proteins, known as ROPs in plants, thought to underly cellular polarity formation. The systems conserve total concentration of each ROP, which enables reduction to simple canonical forms when one seeks conditions for homogeneous equilibria or heteroclinic connections between them. Transitions between different multiplicities of such states are classified using a novel application of catastrophe theory. For the time-dependent problem, the heteroclinic connections represent so-called wave-pinned states that separate regions of the domain with different ROP concentrations. It is shown numerically how the form of wave-pinning reached can be predicted as a function of the domain size and initial total ROP concentrations. This leads to state diagrams of different polarity forms as a function of total concentrations and system parameters.","PeriodicalId":49534,"journal":{"name":"SIAM Journal on Applied Dynamical Systems","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139979658","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

[math]-Reduction, Relative Equilibria, and Bifurcations for the Full Averaged Model of Two Interacting Rigid Bodies [两个相互作用刚体的全平均模型的还原、相对平衡和分岔

IF 2.1 4区数学

SIAM Journal on Applied Dynamical Systems Pub Date : 2024-02-21 DOI: 10.1137/23m158125x

F. Crespo, D. E. Espejo, J. C. van der Meer

{"title":"[math]-Reduction, Relative Equilibria, and Bifurcations for the Full Averaged Model of Two Interacting Rigid Bodies","authors":"F. Crespo, D. E. Espejo, J. C. van der Meer","doi":"10.1137/23m158125x","DOIUrl":"https://doi.org/10.1137/23m158125x","url":null,"abstract":"SIAM Journal on Applied Dynamical Systems, Volume 23, Issue 1, Page 668-695, March 2024. Abstract.We present a geometrical description of the symmetries and reduction of the full gravitational 2-body problem after complete averaging over fast angles. Our variables allow for a well-suited formulation in action-angle type coordinates associated with the averaged angles, which provide geometric insight into the problem. After introducing extra fictitious variables and through a symplectic transformation, we move to a singularity-free quaternionic triple-chart. This choice allows for a global chart to avoid the classical singularities associated with angles and renders all the invariants as homogeneous quadratic polynomials. Additionally, it permits one to quickly write the Hamiltonian of the system in terms of the invariants and the Poisson structure at each stage of the reduction process. In contrast with existing literature, the geometrical approach of this research completely describes all the dynamical aspects of the full reduced space since it involves the relative position of the rotational and orbital angular momenta and their orientation, which has yet to be considered in previous studies. Our program includes a preliminary parametric analysis of relative equilibria and a complete description of the fibers in the reconstruction of the reduced system.","PeriodicalId":49534,"journal":{"name":"SIAM Journal on Applied Dynamical Systems","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139925455","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

Spatio-temporal Dynamics in a Reaction-Diffusion Equation with Nonlocal Spatial Memory 具有非局部空间记忆的反应-扩散方程中的时空动力学

IF 2.1 4区数学

SIAM Journal on Applied Dynamical Systems Pub Date : 2024-02-21 DOI: 10.1137/22m1543860

Shuyang Xue, Yongli Song, Hao Wang

引用次数: 0

Evolution of Dispersal in Advective Patchy Environments with Varying Drift Rates 漂移速率不同的平流斑块环境中的扩散演化

IF 2.1 4区数学

SIAM Journal on Applied Dynamical Systems Pub Date : 2024-02-21 DOI: 10.1137/22m1542027

Shanshan Chen, Jie Liu, Yixiang Wu

引用次数: 0

Connecting Anti-integrability to Attractors for Three-Dimensional Quadratic Diffeomorphisms 将反不可控性与三维二次微分的吸引力联系起来

IF 2.1 4区数学

SIAM Journal on Applied Dynamical Systems Pub Date : 2024-02-06 DOI: 10.1137/23m1571897

Amanda E. Hampton, James D. Meiss

{"title":"Connecting Anti-integrability to Attractors for Three-Dimensional Quadratic Diffeomorphisms","authors":"Amanda E. Hampton, James D. Meiss","doi":"10.1137/23m1571897","DOIUrl":"https://doi.org/10.1137/23m1571897","url":null,"abstract":"SIAM Journal on Applied Dynamical Systems, Volume 23, Issue 1, Page 616-640, March 2024. Abstract. We previously showed that three-dimensional quadratic diffeomorphisms have anti-integrable (AI) limits that correspond to a quadratic correspondence, a pair of one-dimensional maps. At the AI limit the dynamics is conjugate to a full shift on two symbols. Here we consider a more general AI limit, allowing two parameters of the map to go to infinity. We prove the existence of AI states for each symbol sequence for three cases of the quadratic correspondence: parabolas, ellipses, and hyperbolas. A contraction argument gives parameter domains such that this is a bijection, but the correspondence also is observed to apply more generally. We show that orbits of the original map can be obtained by numerical continuation for a volume-contracting case. These results show that periodic AI states evolve into the observed periodic attractors of the diffeomorphism. We also continue a periodic AI state with a symbol sequence chosen so that it continues to an orbit resembling a chaotic attractor that is a 3D version of the classical 2D Hénon attractor.","PeriodicalId":49534,"journal":{"name":"SIAM Journal on Applied Dynamical Systems","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139770434","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

A Unified Approach to Reverse Engineering and Data Selection for Unique Network Identification 逆向工程和数据选择的统一方法，用于唯一网络识别

IF 2.1 4区数学

SIAM Journal on Applied Dynamical Systems Pub Date : 2024-02-05 DOI: 10.1137/22m1540570

Alan Veliz-Cuba, Vanessa Newsome-Slade, Elena S. Dimitrova

引用次数: 0