Nonlinear Dynamics of Oscillator Networks

振荡器网络的非线性动力学

• 批准号: 0078074
• 负责人: Steven Strogatz
• 金额: $ 31.2万
• 依托单位: Cornell University
• 依托单位国家: 美国
• 项目类别: Continuing grant
• 财政年份: 2000
• 资助国家: 美国
• 起止时间: 2000-09-01 至 2003-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0078074&HistoricalAwards=false
• 关键词: Nonlinear; Dynamics; Oscillator; Networks

Strogatz0078074 In several branches of science and technology, one likewould like to imitate nature's success at designing networks thatcan synchronize themselves. For instance, a semiconductor laserarray generates greater collective power when it synchronizes,but such phase-locked operation is notoriously difficult toachieve in practice. The investigator studies the nonlineardynamics of oscillator networks, using mathematical methods ofdynamical systems theory, bifurcation theory, and statisticalmechanics, along with numerical simulation. Three projectsexplore how synchrony emerges in a group of dissimilaroscillators, motivated by both biological and laser applications.Areas of investigation include the stability of partial lockingin the Kuramoto model of coupled biological oscillators; thedynamics of biological oscillators coupled by phase-responsecurves; and phase-locking in slightly detuned laser arrays. Twoother projects address the relation between the connectivity of anetwork and its ability to synchronize. Small-world networks,which combine small diameter with large clustering, areinvestigated to test whether they synchronize more readily thanlattices. The goal of this project is to develop a deeperunderstanding of complex systems that are made of manyoscillating parts and that manage to synchronize themselves. Forinstance, the thousands of pacemaker cells in the heart alwaysfire in unison, even though they are all slightly different fromone another. Unfortunately, a similar kind of coordinationsometimes happens in the brain, where it leads to epilepsy. Inboth cases, nature has provided us with examples in whichmillions of cells begin to act in unison. By understandingbetter how this synchrony is achieved, it should be possible todesign arrays of technologically important devices that cansynchronize themselves. Such self-synchronizing systems wouldhave important technological applications in many areas ofnational interest, including environment (atmospheric pollutionmonitoring uses sensitive detectors based on arrays ofoscillators), civil infrastructure (the proper functioning of thenational power grid depends on self-synchronization of thegenerator network), and nanotechnology (where arrays of millionsof microscopic mechanical oscillators are being used in newdevices).

Strogatz0078074 在科学技术的几个分支中，人们希望模仿大自然在设计可以自我同步的网络方面的成功。 例如，半导体激光器阵列在同步时会产生更大的集体功率，但众所周知，这种锁相操作在实践中很难实现。 研究人员利用动力系统理论、分岔理论和统计力学的数学方法以及数值模拟来研究振荡器网络的非线性动力学。 三个项目探索在生物和激光应用的推动下，一组不同振荡器中如何出现同步。研究领域包括耦合生物振荡器 Kuramoto 模型中部分锁定的稳定性；相位响应耦合的生物振荡器的动力学；以及轻微失谐激光阵列中的锁相。 另外两个项目解决了网络连接性与其同步能力之间的关系。 研究将小直径与大集群相结合的小世界网络，以测试它们是否比晶格更容易同步。 该项目的目标是更深入地了解由许多振荡部件组成并设法实现自身同步的复杂系统。 例如，心脏中的数千个起搏细胞总是一致放电，尽管它们彼此之间略有不同。 不幸的是，类似的协调有时会发生在大脑中，从而导致癫痫。 在这两种情况下，大自然都为我们提供了数以百万计的细胞开始协同行动的例子。 通过更好地理解这种同步是如何实现的，应该可以设计出具有技术重要性的、能够自我同步的设备阵列。 这种自同步系统将在许多国家利益领域具有重要的技术应用，包括环境（大气污染监测使用基于振荡器阵列的灵敏探测器）、民用基础设施（国家电网的正常运行取决于发电机网络的自同步）和纳米技术（数以百万计的微型机械振荡器阵列被用于新设备）。