Nonlinear Dynamics of Oscillator Networks

Cornell University, Ithaca NY

Investigators

Abstract

Strogatz 0078074 In several branches of science and technology, one like would like to imitate nature's success at designing networks that can synchronize themselves. For instance, a semiconductor laser array generates greater collective power when it synchronizes, but such phase-locked operation is notoriously difficult to achieve in practice. The investigator studies the nonlinear dynamics of oscillator networks, using mathematical methods of dynamical systems theory, bifurcation theory, and statistical mechanics, along with numerical simulation. Three projects explore how synchrony emerges in a group of dissimilar oscillators, motivated by both biological and laser applications. Areas of investigation include the stability of partial locking in the Kuramoto model of coupled biological oscillators; the dynamics of biological oscillators coupled by phase-response curves; and phase-locking in slightly detuned laser arrays. Two other projects address the relation between the connectivity of a network and its ability to synchronize. Small-world networks, which combine small diameter with large clustering, are investigated to test whether they synchronize more readily than lattices. The goal of this project is to develop a deeper understanding of complex systems that are made of many oscillating parts and that manage to synchronize themselves. For instance, the thousands of pacemaker cells in the heart always fire in unison, even though they are all slightly different from one another. Unfortunately, a similar kind of coordination sometimes happens in the brain, where it leads to epilepsy. In both cases, nature has provided us with examples in which millions of cells begin to act in unison. By understanding better how this synchrony is achieved, it should be possible to design arrays of technologically important devices that can synchronize themselves. Such self-synchronizing systems would have important technological applications in many areas of national interest, including environment (atmospheric pollution monitoring uses sensitive detectors based on arrays of oscillators), civil infrastructure (the proper functioning of the national power grid depends on self-synchronization of the generator network), and nanotechnology (where arrays of millions of microscopic mechanical oscillators are being used in new devices).