Ott: Dynamics of Large Systems of Many Coupled...
Oct
20
Mon 4:00 PM
When Monday, October 20, 2008
Time
4:00 PM - 5:00 PM
Where Tech M416
Contact Molly Scanlon
847-491-5586
Group McCormick-Colloquia Engineering Sciences and Applied Mathematics
Applied Math Colloquium
Title: Dynamics of Large Systems of Many Coupled Oscillators: Low Dimensional Behavior and Applications
Speaker: Edward Ott, University of Maryland
Abstract: Large systems of many coupled oscillators occur frequently in a wide variety of natural settings. A central question is whether and to what degree these systems display global synchronous dynamics. Examples where this issue arises include pacemaker cells in the heart, the observed synchronization of pedestrians walking on London's Millenium Bridge which resulted in unwanted wobble of the bridge, brain function, the interaction of neurons that govern circadian rythm in mammals, oscillations in bubbly fluids, etc. For such situations the simple paradigmatic Kuramoto model has played a key role in facilitating understanding. This talk will present a nonlinear, exact solution to the Kuramoto model in the limit of an infinite number of oscillators. The technique employed [1] essentially reduces the infinite dimensional problem to a low dimensional one. Then, it will be shown how our technique can be extended for application to a wide class of more realistic and complex problems. As an example, recent results applying the method to the Millenium Bridge problem will be presented.
Title: Dynamics of Large Systems of Many Coupled Oscillators: Low Dimensional Behavior and Applications
Speaker: Edward Ott, University of Maryland
Abstract: Large systems of many coupled oscillators occur frequently in a wide variety of natural settings. A central question is whether and to what degree these systems display global synchronous dynamics. Examples where this issue arises include pacemaker cells in the heart, the observed synchronization of pedestrians walking on London's Millenium Bridge which resulted in unwanted wobble of the bridge, brain function, the interaction of neurons that govern circadian rythm in mammals, oscillations in bubbly fluids, etc. For such situations the simple paradigmatic Kuramoto model has played a key role in facilitating understanding. This talk will present a nonlinear, exact solution to the Kuramoto model in the limit of an infinite number of oscillators. The technique employed [1] essentially reduces the infinite dimensional problem to a low dimensional one. Then, it will be shown how our technique can be extended for application to a wide class of more realistic and complex problems. As an example, recent results applying the method to the Millenium Bridge problem will be presented.
