Nonlinear Dynamics of Oscillator Networks

斯特罗加茨0078074 在科学和技术的几个分支中，人们想模仿自然界成功地设计出能够自我同步的网络。 例如，半导体激光器阵列在振荡时产生更大的集体功率，但这种锁相操作在实践中是非常难以实现的。 研究者运用动力系统理论、分岔理论、动力学力学的数学方法，沿着数值模拟，研究振荡器网络的非线性动力学。 三个项目探讨了如何同步出现在一组dissimilaroscillator，由生物和激光应用的动机。研究领域包括耦合生物振荡器的Kuramoto模型的部分锁定的稳定性;生物振荡器的动力学耦合的相位响应安全;和相位锁定在轻微失谐的激光阵列。 另外两个项目致力于研究网络的连通性和同步能力之间的关系。 小世界网络，结合联合收割机小直径与大集群，被调查，以测试他们是否更容易同步比格子。 这个项目的目标是开发一个复杂的系统，是由许多振荡部件，并设法同步自己更深入的理解。 例如，心脏中成千上万的起搏细胞总是一致地放电，即使它们彼此之间都略有不同。 不幸的是，类似的协调有时会发生在大脑中，在那里它会导致癫痫。 在这两种情况下，大自然都为我们提供了数百万个细胞开始一致行动的例子。 通过更好地理解这种同步是如何实现的，应该有可能设计出一系列具有重要技术意义的设备，它们可以实现自身同步。 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敏感探测器），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（数百万微观机械振荡器阵列正在用于新设备）。

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).