Math 485 -- Mathematical Modeling
Synchronous behavior in living organisms
London's Millennium Bridge
London's Millennium Bridge opened on June 10, 2000. An estimated 80,000 to 100,000 people crossed it. The bridge began swaying as the crowd built up. The following paper provides an explanation.
- Video from opening day
- Crowd synchrony on London's Millennium Bridge by S H Strogatz, D M Abrams, A McRobie, B Eckhardt, and E Ott. Nature 438 (2005) pp 43-44
Synchronous flashing of fireflies
Some species of fireflies (notably some in Southeaste Asia and in the Smoky Mountains here in the US) have been observed to flash in unison. The following paper provides an explanation for this and other synchronization phenomena in biology in terms of a simple mathematical model.Note: The paper is a bit more mathematical than the others listed, but the phenomenon in question is quite accessible to simulations.
- A video of fireflies flashing
- Synchronous flashing of fireflies by S H Strogatz and R Mirollo. SIAM J. Appl. Math. 50 (1990) pp 1645-1662
- An adaptive model for synchrony in the firefly Pteroptyx malaccae by G B Ermentrout. J. Math. Bio. 29 (1991) pp 571-585
- Nonlinear Dynamics and Chaos by Steven
H. Strogatz (Addison-Wesley 1994) is a good reference for
the nonlinear dynamics aspects of this problem.
- A recent New York Times article on synchronization