Mathematical Biology: Nonlinear Dynamics of Oscillator Networks

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StrogatzMany populations of biological oscillators can exhibit remarkablecollective behavior. Despite differences in their individualnatural frequencies, the oscillators spontaneously synchronize toa common frequency. Examples include chorusing crickets,fireflies that flash in unison, and synchronous firing of cardiacpacemaker cells. In several other branches of science andtechnology, one would like to imitate nature's success atdesigning networks that can synchronize themselves. Forinstance, a semiconductor laser array generates greatercollective power when it synchronizes, but such phase-lockedoperation is notoriously difficult to achieve in practice. ThePI and his students study the dynamics of oscillator networks,using mathematical methods of dynamical systems theory,bifurcation theory, and statistical mechanics, along withnumerical simulation. One project investigates a peculiarmathematical phenomenon that was recently discovered in a modelof cellular oscillators communicating with one another throughthe exchange of a signaling molecule. Three additional projectsventure into areas where oscillator theory has rarely beenapplied, namely molecular genetics, stochastic analysis, and theinterplay of human behavior and civil engineering. The goal ineach case is to answer a mathematically fascinating question thatis important in the real world. Specifically: (1) How can onebuild the analog of a multicellular biological clock, usingsynthetic gene circuits? (2) Can a precise biological clock bemade by synchronizing many imprecise components, and is this whattakes place in our own circadian pacemakers? (3) What causedLondon's Millennium Bridge to wobble on opening day? Each ofthese projects enlists the collaboration of a top experimentalistin the relevant field.Networks of oscillators arise throughout science and technologyand are ubiquitous in nature: lasers arrays work better when theyoscillate synchronously, structures such as buildings and bridgescan be endangered by synchronous oscillation, synchronous firingof cardiac pacemaker cells keeps hearts beating. Theinvestigator mathematically explores the behavior of networks ofoscillators, studying how networks synchronize themselves. Benefits are expected for the understanding of how rhythmicallyactive cells work together in tissues and organs; for thecharacterization of the potentially dangerous ways that crowds ofpedestrians can inadvertently cause footbridges to shake; and forspin-offs to technological applications involving arrays ofoscillators, such as lasers, microwave oscillators, andsuperconducting Josephson junctions. By training three graduatestudents through the research opportunities offered here, thisproject also helps to develop human resources that are vital toour nation's success in science and engineering.