Temporal and Spatio-Temporal Forcing of Oscillatory and Excitable Systems

振荡和可兴奋系统的时间和时空强迫

• 批准号: 0309667
• 负责人: Mary Silber
• 金额: --
• 依托单位: Northwestern University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2003
• 资助国家: 美国
• 起止时间: 2003-07-15 至 2008-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0309667&HistoricalAwards=false
• 关键词: Temporal; Spatio; Forcing; Oscillatory; Excitable

Proposal: DMS-0309667PI: David Mary Silber [[e-mail]]Institution: Northwestern UniversityTitle: Temporal and Spatio-Temporal Forcing of Oscillatory and Excitable SystemsABSTRACTThe investigator, together with students and colleagues, studies three problems in which temporal or spatio-temporal forcing of oscillatory or excitable systems is important: (1) parametrically excited surface wave patterns, (2) spatio-temporal local feedback in pattern forming systems, and (3) Hopf bifurcation based mechanisms for amplification of sound by inner ear hair cells. Faraday waves, excited on the free surface of a fluid, form in a wide variety of patterns depending on the fluid properties and the form of the periodic forcing function. The investigator's research program focuses on a bifurcation analysis of three- and four-wave interactions when a periodic sequence of delta-function impulses is applied to the fluid container. This idealized forcing function admits unprecedented analytic progress to be made in the linear and weakly nonlinear regimes that apply at or near onset of instability. This project probes how the periodic forcing function may be designed to favor particular patterns. In the second research project spatio-temporal feedback is used to probe the nonlinear pattern formation process, as well as to actively control it. The control of spatio-temporal patterns by local time-delayed and spatially-transformed feedback will be investigated through linear stability analysis, equivariant bifurcation theory, and numerical simulation. In the third project, models of inner ear hair cells, responsible for translating sound-induced motion into electrical signals, are analysed. The initial focus is on amphibian hair cells, for which two separate mechanisms that contribute to the cells' frequency selectivity have been identified - one due to active mechanical motions of the hair bundle and the other captured by an electrochemical model of ion channels in the hair cell body. In each model proximity to a Hopf bifurcation contributes to the amplification properties of the hair cells. The investigator's research project uses dynamical systems methods to derive a reliable reduced model, from existing detailed physiological models of the two Hopf bifurcation mechanisms, with attention to the effects of this two-stage amplification on gain and frequency selectivity. This project lays the foundation for further investigation of the effects of coupling the hair cell bundles.Many spatially extended nonlinear systems, including hydrodynamic and laser systems, exhibit spatio-temporal chaotic behavior when subjected to external forcing. The investigator's research program will lead to a deeper understanding of how to eliminate irregular behavior in favor of spatio-temporally regular patterns. This is done through appropriate design of the temporal forcing function in the case of hydrodynamic waves, or through spatio-temporal feedback in the case of nonlinear optical and chemical systems. Careful comparison between theoretical results and results of experimental investigations will be made, providing valuable feedback to this research effort. The investigator's analysis of biophysical models of inner ear hair cells contributes to a greater understanding of how the nonlinearities in two proposed mechanisms of frequency selectivity and amplification might work together to achieve greater gain. The training of applied mathematics graduate students and postdoctoral fellows in interdisciplinary research activities is an integral part of the research effort.

提案：DMS-0309667PI：David Mary Silber [[e-mail]]机构：西北大学大学：暂时和时空的强迫强迫振动性和令人兴奋性的系统消除研究者，研究人员与学生和同事一起研究三个问题，其中包括临时或spatio spatio-steral isosc oscect of Osscort occtio oscect of occtio oscect of occation orcorter ocction oscect of（（激发的表面波模式，（2）模式形成系统中的时空局部反馈，以及（3）基于HOPF分叉的机制，用于通过内耳毛细胞扩增声音。 Faraday波在流体的自由表面上激发，根据流体特性和周期性强迫函数的形式形成多种模式。当将Delta功能冲动的周期性序列应用于流体容器时，研究者的研究计划重点介绍了三波相互作用的分叉分析。这种理想化的强迫函数允许在适用于不稳定性或接近发作的线性和弱非线性方案中取得前所未有的分析进度。 该项目探讨了如何设计定期强迫函数以偏爱特定模式。在第二个研究项目中，时空反馈用于探测非线性模式形成过程，并积极控制它。将通过线性稳定性分析，等效分叉理论和数值模拟来研究通过局部延迟和空间转换的反馈来控制时空模式的控制。在第三个项目中，分析了内耳毛细胞的模型，负责将声音诱导的运动转化为电信号。 最初的重点是两栖毛细胞，为此，已经确定了有助于细胞频率选择性的两种独立机制 - 一个是由于毛发束的主动机械运动，另一个是由毛细胞体中离子通道的电化学模型捕获的。 在每个模型中，与HOPF分叉的接近性有助于毛细胞的扩增特性。 研究者的研究项目使用动力学系统方法来从两种HOPF分叉机制的现有详细生理模型中得出可靠的减少模型，并注意这种两阶段扩增对增益和频率选择性的影响。 该项目奠定了基础，以进一步研究耦合毛细胞束的影响。当受到外部强迫时，许多空间扩展的非线性系统（包括流体动力和激光系统）表现出时空混乱的行为。 研究者的研究计划将对如何消除不规则行为有利于时髦的规则模式有更深入的了解。 在非线性光学和化学系统的情况下，在流体动力波的情况下，或通过时空反馈进行适当设计，可以通过适当设计时间强迫函数来完成。将进行理论结果和实验研究结果之间的仔细比较，为这项研究工作提供宝贵的反馈。 研究者对内耳毛细胞生物物理模型的分析有助于更了解对两种频率选择性和扩增机制中的非线性如何共同起作用，以实现更大的增益。 跨学科研究活动中应用数学研究生和博士后研究员的培训是研究工作不可或缺的一部分。