Synchronizing Fireflies

Synchronizing Fireflies

Author(s): Ying Zhou, Walter Gall and Karen Nabb

College Mathematics Journal, Vol. 37, No. 3 (May, 2006), pp. 187-193

Published by: Mathematical Association of America

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This paper provides an excellent example of the importance of qualitative analysis when modeling with differential equations. It is now known in biology that in some parts of the world (e.g., Thailand, or, to a lesser extent, small regions in the USA) male fireflies will flash simultaneously to attract females or that crickets will chirp in unison. The authors propose a mathematical model to explain how two fireflies synchronize their flashing. They first explain the idea of a biological clock and then develop a system of two nonlinear equations to explain how fireflies flash. This system can be reduced to a single nonlinear equation, and the equilibrium points can be analyzed for stability to conclude that the fireflies will eventually synchronize their flashing. Thomas W. Judson, Stephen F. Austin State University, March 31, 2013.

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