Coupled Systems and Applications

耦合系统和应用

• 批准号: 1008412
• 负责人: Martin Golubitsky
• 金额: $ 20.12万
• 依托单位: Ohio State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-07-01 至 2014-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1008412&HistoricalAwards=false
• 关键词: Coupled; Systems; Applications

The principal investigator and his students and collaborators study the dynamics of networks of systems of differential equations and their applications. Previous work identified when network architecture forces synchrony to be present in such systems (generalizing network symmetry to a combinatorial notion of a balanced coloring). Balanced colorings also lead to quotient networks and previous work also showed that robust phase shift synchrony can be associated to symmetry in a quotient network. These theories were motivated by studies of locomotor central pattern generators of animal gaits. The studies have progressed and several general questions are now studied like: Are all robust phase shifts present in periodic solutions of network equations the result of symmetry (using quotient networks), what are the patterns of oscillations associated with network architecture, and do these patterns always appear through bifurcation? (Surprisingly the answer to the last question is no; additionally, network architecture can change Hopf bifurcation in ways that transcend symmetry.) How network dynamics affects Takens reconstruction is studied (is it possible to reconstruct network dynamics from the output of one node) and the dynamics of small networks (can general network studies lead to a better understanding of motifs in Systems Biology) is studied.The study of networks of differential equations is central to much of modern biology (from biochemical networks through protein interaction networks and gene transcription networks to ecology through food webs). Recent work by many research groups (usually based on chemical kinetics equations) has shown that network architecture does affect the kind of solutions that appear in coupled systems. Moreover, these solutions lead to function and to conjectures about how large biological networks work. General mathematical studies of network dynamics are providing both the tools needed to investigate more specific networks and an understanding of the kinds of phenomena that network models can produce. The project involves studying general theories for network dynamics, specific examples of networks that promise to yield new (mathematical) phenomena, and specific application areas (such as the ways in which sound waves are processed in the cochlear region of the inner ear, which in part is based on a network model of inner hair bundles).

首席研究员和他的学生和合作者研究微分方程系统网络的动力学及其应用。以前的工作确定了网络架构何时迫使同步出现在这样的系统中（将网络对称推广到平衡着色的组合概念）。平衡着色也会导致商网络，以前的工作也表明，鲁棒相移同步可以与商网络中的对称性相关联。这些理论是由对动物步态的运动中枢模式发生器的研究所激发的。研究取得了进展，现在研究了几个一般问题，如：在网络方程的周期解中存在的所有鲁棒相移是否都是对称的结果（使用商网络），与网络结构相关的振荡模式是什么，这些模式是否总是通过分岔出现？（令人惊讶的是，最后一个问题的答案是否定的；此外，网络架构可以以超越对称性的方式改变Hopf分岔。）研究了网络动力学如何影响Takens重建（是否有可能从一个节点的输出重建网络动力学）和小网络的动力学（一般网络研究是否可以更好地理解系统生物学中的基序）。微分方程网络的研究是现代生物学的核心（从生物化学网络到蛋白质相互作用网络和基因转录网络，再到生态学到食物网）。许多研究小组最近的工作（通常基于化学动力学方程）表明，网络架构确实会影响耦合系统中出现的解决方案的类型。此外，这些解决方案导致了对大型生物网络如何工作的功能和猜测。网络动力学的一般数学研究既提供了研究更具体的网络所需的工具，也提供了对网络模型可能产生的各种现象的理解。该项目包括研究网络动力学的一般理论，有望产生新（数学）现象的网络的具体例子，以及特定的应用领域（如内耳耳蜗区域处理声波的方式，部分是基于内耳毛束的网络模型）。