Nonlinear Dynamics of Oscillator Networks

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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).