Modeling and Control of Pattern-Forming Dynamical Systems

模式形成动力系统的建模和控制

• 批准号: 0639749
• 负责人: Chad Topaz
• 金额: $ 20.97万
• 依托单位: University of Southern California
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-09-01 至 2007-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0639749&HistoricalAwards=false
• 关键词: Modeling; Control; Pattern; Forming; Dynamical

The investigator studies biological and chemical systems that form spatiotemporal patterns. One research project focuses on the modeling and analysis of locust swarms. Locusts can operate in either a solitary (neighbor-avoiding) or gregarious (neighbor-seeking) phase. The investigator constructs a PDE model incorporating social aspects of behavior as well as environmental variables and random motion in order to understand how each of these factors affects the dynamics of phase change, the spatial patterns of the locust population, and the nucleation of gregarious groups. A second model describes the rolling motion of migrating gregarious groups. The high-dimensional ODE model incorporates social interactions, gravity, wind, and the boundary formed by the ground. The models are studied with tools from dynamical systems, statistical mechanics, analysis of PDE, and numerical simulation. Another project examines the control of Turing patterns in chemical reaction-diffusion systems. Inspired by recent experiments which controlled chemical Turing patterns by using an external light field, the investigator develops a framework for manipulating reaction-diffusion patterns via periodic spatiotemporal forcing. The study is built around a symmetry-based analysis of normal forms, a perturbation analysis of reaction-diffusion type PDE, and numerical simulations, all of which reveal how pattern stability is affected by the applied forcing.Spatiotemporal pattern formation occurs spontaneously in myriad natural systems. Key challenges include the development of mathematical models of these systems, the analysis of the models, and the development of methods for controlling the patterns. The investigator's research on locust plagues primarily addresses the first two challenges. Locusts are an important pattern-forming biological systems because their destructive swarms have severe environmental and economic impacts. Some results are general enough to shed light on other social biological aggregations such as bird flocks and fish schools. The research on Turing patterns in chemical systems addresses the third challenge. The results explain experimental observations and suggest control strategies that can be tested in the lab. Furthermore, some of the results apply to other Turing patterns, which occur in such diverse contexts as biological morphogenesis, population dynamics, neuroscience, ecology, and materials science. The training and mentoring of research students and the development of math and science instruction using novel pedagogical techniques all play a key role in the investigator's program.

研究者研究形成时空模式的生物和化学系统。一个研究项目侧重于蝗虫群的建模和分析。蝗虫可以在孤独（避免邻居）或群居（寻找邻居）阶段活动。研究人员构建了一个PDE模型，将社会方面的行为，以及环境变量和随机运动，以了解这些因素如何影响动态的相变，蝗虫种群的空间格局，和群居群体的成核。第二个模型描述了迁移群居群体的滚动运动。高维ODE模型包含了社会互动、重力、风和地面形成的边界。该模型的研究工具，从动力系统，统计力学，偏微分方程的分析，数值模拟。另一个项目研究了化学反应扩散系统中图灵模式的控制。受最近通过使用外部光场控制化学图灵模式的实验的启发，研究人员开发了一个通过周期性时空强迫操纵反应扩散模式的框架。本研究是建立在一个基于mathery的分析规范的形式，扰动分析的反应扩散型偏微分方程，和数值模拟，所有这些都揭示了图案的稳定性是如何影响所施加的forcing.Spatiotemporal图案的形成自发地发生在无数的自然系统。主要的挑战包括这些系统的数学模型的发展，模型的分析，以及控制模式的方法的发展。调查员对蝗灾的研究主要针对前两个挑战。蝗虫是一种重要的模式形成生物系统，因为它们的破坏性群体具有严重的环境和经济影响。一些结果是一般性的，足以阐明其他社会生物聚集，如鸟群和鱼群。对化学系统中图灵模式的研究解决了第三个挑战。这些结果解释了实验观察结果，并提出了可以在实验室中进行测试的控制策略。此外，一些结果适用于其他图灵模式，这些模式发生在生物形态发生，种群动力学，神经科学，生态学和材料科学等不同的背景下。研究生的培训和指导以及使用新的教学技术发展数学和科学教学都在研究者的计划中发挥着关键作用。