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.

这项赠款将支持将促进物理，化学和生物科学进展的研究，从而增强民族健康和繁荣。 在过去的四分之一世纪中，超级计算功能的快速进步导致计算模型的规模和复杂性爆炸。 减少模型是数学分析和随后在这些复杂和高维系统中主动控制策略的急需初步步骤。 不幸的是，现有的还原策略缺乏能力，无法理解有关动态行为的定性变化的机制，尤其是当潜在行为以系统非线性为主时。 该奖项支持将开发数学还原策略的基础研究，这些策略可用于预测和工程师在高维非线性动力学系统的行为中所需的改变。 这些新方法将在多种应用中找到使用，例如心脏电生理学，神经网络和流体流，从而对国家健康和安全产生了益处。 重要的研究结果将纳入教育计划中，从而使学生从代表性不足的背景中受益。该项目的目的是研究如何使用新开发的同样减少框架来预测和设计高维非线性动力学系统中的分叉。 同位还原方法明确纳入了主要的系统非线性，同时保持分析性障碍。因此，它复制了建立的线性还原策略不能做到的系统行为。 作为这项研究的一部分，将创建新的非反馈控制框架，可用于稳定任意高维的混乱和不稳定的动力系统。 此外，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的分叉。 还将制定策略来推断实验应用中等值降低方程的必要条款，这些方程将允许在系统中未知的基础模型方程的系统中实施这些还原策略。 该项目中的主要应用是在追求更好疾病治疗方案的心脏和神经电生理学模型中。该奖项反映了NSF的法定任务，并使用基金会的知识分子优点和更广泛的影响评估审查标准，认为值得通过评估来获得支持。

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

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.

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

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