One of nature's most amazing sights is the rhythmic, synchronized flashing of thousands upon thousands of fireflies on riverbanks in Southeast Asia. This is a particularly dramatic example of a general phenomenon that has been garnering more and more attention from scientists: The ability of individual rhythmic elements of all sorts—fireflies, clocks, pacemaker cells of the heart, neurons of the brain—to synchronize with one another. I will review the development of our current understanding of synchronization, which dates back to Huygens, and emphasize the pioneering work of Winfree, Kuramoto, Strogatz, and others. This leads to the larger question of how more general collective behavior emerges from large collections of interacting elements. Finally, I will review our own work in the biological context of interacting neurons.
Paul So is theoretical physicist specializing in nonlinear dynamics. He obtained his PhD from the Chaos Group at the University of Maryland. His previous work includes development of control theory for high dimensional chaotic systems, theory and experimental work in quantum chaos, identification and characterization of synchronization in chaotic systems, and dynamical reconstruction using both observer techniques and unstable periodic orbits. His roles in the George Mason University Krasnow Institute for Advanced Studies Neural Dynamics Laboratory include development of new theoretical understanding of dynamical systems, the development of new analysis techniques for nonlinear systems, and their application to neuronal data.
Ernest Barreto works on nonlinear dynamics and chaos. He also obtained his PhD from the Chaos Group at the University of Maryland. Recent interests include emergence in coupled maps, control and synchronization of chaotic systems, the structure of the parameter space of such systems, and shadow ability (which involved the relationship between numerical simulations and mathematically accurate solutions). He is also affiliated with the Neural Dynamics Laboratory, applying nonlinear dynamics methods to the study of neuronal systems and EEG data. He was the third-place male grand champion in the 2002 International Whistler's Convention, with a performance of the Adagio and Rondo movements of the Mozart Flute Quartet in D.
Paul So and Ernest Barreto work collaboratively on the topics of nonlinear dynamics, chaos, and neural dynamics.
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