Engineering Bifurcations in High-Dimensional Dynamical Systems Using Isostable Reduction Methods

使用等稳定约简方法在高维动力系统中设计分岔

• 批准号: 1933583
• 负责人: Dan Wilson
• 金额: $ 32.05万
• 依托单位: University of Tennessee Knoxville
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2020
• 资助国家: 美国
• 起止时间: 2020-01-01 至 2023-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1933583&HistoricalAwards=false
• 关键词: Engineering; Bifurcations; Dimensional; Dynamical; Systems

This grant will support research that will promote progress in the physical, chemical, and biological sciences thereby enhancing national health and prosperity. Over the past quarter century rapid progress of supercomputing capabilities has resulted in an explosion in the size and complexity of computational models. Model reduction is an imperative preliminary step in the mathematical analysis and subsequent implementation of active control strategies in these complex and high-dimensional systems. Unfortunately, existing reduction strategies are ill-equipped to understand the mechanisms governing qualitative changes in dynamical behavior, particularly when the underlying behavior is dominated by system nonlinearities. This award supports fundamental research that will develop mathematical reduction strategies that can be used to anticipate and engineer desired changes in the behavior of high-dimensional, nonlinear dynamical systems. These new methods will find use in a wide variety of applications such as cardiac electrophysiology, neural networks, and fluid flows with resulting benefits to national health and security. Important research findings will be incorporated into educational programs that benefit students from underrepresented backgrounds.The goal of this project is to study how a newly developed isostable reduction framework can be used to predict and engineer bifurcations in high-dimensional, nonlinear dynamical systems. The isostable reduction approach explicitly incorporates dominant system nonlinearities while retaining analytical tractability; as such it replicates system behaviors that well-established linear reduction strategies cannot. As part of this research, novel nonfeedback control frameworks will be created that can be used to stabilize chaotic and unstable dynamical systems of arbitrarily high dimension. Additionally, mathematical frameworks will be created to anticipate bifurcations that lead to the onset of spontaneous synchronization in strongly coupled oscillator networks. Strategies will also be developed to infer the necessary terms of isostable reduced equations in experimental applications which will allow for the implementation of these reduction strategies in systems for which the underlying model equations are not explicitly known. The primary applications in this project will be to models of cardiac and neural electrophysiology in pursuit of better disease treatment options.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

这笔赠款将支持促进物理、化学和生物科学进步的研究，从而促进国民健康和繁荣。 在过去的四分之一个世纪里，超级计算能力的快速进步导致计算模型的规模和复杂性呈爆炸式增长。 模型简化是这些复杂高维系统中主动控制策略的数学分析和后续实施中必不可少的初步步骤。 不幸的是，现有的还原策略不足以理解控制动态行为质变的机制，特别是当潜在行为由系统非线性主导时。 该奖项支持基础研究，这些研究将开发数学简化策略，可用于预测和设计高维非线性动力系统行为的所需变化。 这些新方法将广泛应用于心脏电生理学、神经网络和流体流动等领域，从而为国家健康和安全带来好处。 重要的研究成果将被纳入教育计划中，使来自代表性不足的背景的学生受益。该项目的目标是研究如何使用新开发的等稳态还原框架来预测和设计高维非线性动力系统中的分岔。 等稳态还原方法明确地结合了主要系统非线性，同时保留了分析的易处理性；因此，它复制了完善的线性归约策略无法复制的系统行为。 作为这项研究的一部分，将创建新颖的无反馈控制框架，可用于稳定任意高维的混沌和不稳定动力系统。 此外，还将创建数学框架来预测导致强耦合振荡器网络中自发同步开始的分叉。 还将开发策略来推断实验应用中等稳态简化方程的必要项，这将允许在未明确了解基础模型方程的系统中实施这些简化策略。 该项目的主要应用将是心脏和神经电生理学模型，以寻求更好的疾病治疗方案。该奖项反映了 NSF 的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。

项目成果

Optimal open-loop desynchronization of neural oscillator populations

神经振荡器群的最佳开环去同步化

• DOI: 10.1007/s00285-020-01501-1
• 发表时间: 2020
• 期刊: Journal of Mathematical Biology
• 影响因子: 1.9
• 作者: Wilson, Dan

Degenerate isostable reduction for fixed-point and limit-cycle attractors with defective linearizations

具有缺陷线性化的定点和极限环吸引子的简并等稳态约简

• DOI: 10.1103/physreve.103.022211
• 发表时间: 2021
• 期刊: Physical Review E
• 影响因子: 2.4
• 作者: Wilson, Dan

Analysis of input-induced oscillations using the isostable coordinate framework

使用等稳态坐标框架分析输入引起的振荡

• DOI: 10.1063/5.0036508
• 发表时间: 2021
• 期刊: Chaos: An Interdisciplinary Journal of Nonlinear Science
• 作者: Wilson, Dan

Adaptive Isostable Reduction of Nonlinear PDEs With Time Varying Parameters

具有时变参数的非线性偏微分方程的自适应等稳态约简

• DOI: 10.1109/lcsys.2020.3001439
• 发表时间: 2021
• 期刊: IEEE Control Systems Letters
• 影响因子: 3
• 作者: Wilson, Dan;Djouadi, Seddik M.
• 通讯作者: Djouadi, Seddik M.

A data-driven phase and isostable reduced modeling framework for oscillatory dynamical systems

振荡动力系统的数据驱动相和等稳态简化建模框架

• DOI: 10.1063/1.5126122
• 发表时间: 2020
• 期刊: Chaos: An Interdisciplinary Journal of Nonlinear Science
• 作者: Wilson, Dan